Function Composition

Key Questions

• Is function composition associative?

  Answer:

  Yes

  Explanation:

  Given composable functions `f`, `g` and `h`

  `(f@(g@h))(x)`

  `= f((g@h)(x)) = f(g(h(x))) = (f@g)(h(x))`

  `= ((f@g)@h)(x)`

  So `f@(g@h) = (f@g)@h`

  George C. · 1 · Jul 24 2015
• What is the domain of `(f@g)(x)`?

  Answer:

  If `g:A->B` and `f:B->C`, then the domain of `f@g` is

  `bar(g)^(-1)@bar(f)^(-1)(C)`

  using the notation described below...

  Explanation:

  If `g` is a function that maps some elements of a set `A` to elements of a set `B`, then the domain of `g` is the subset of `A` for which `g(a)` is defined.

  More formally:

  `g sube A xx B :`

  `AA a in A AA b_1, b_2 in B`

  `((a, b_1) in g ^^ (a, b_2) in g) => b_1 = b_2`

  Use the notation `2^A` to represent the set of subsets of `A` and `2^B` the set of subsets of `B`.

  Then we can define the pre-image function:

  `bar(g)^(-1): 2^B -> 2^A` by `bar(g)^(-1)(B_1) = {a in A : g(a) in B_1}`

  Then the domain of `g` is simply `bar(g)^(-1)(B)`

  If `f` is a function that maps some elements of set `B` to elements of a set `C`, then:

  `bar(f)^(-1): 2^C -> 2^B` is defined by `bar(f)^(-1)(C_1) = {b in B : f(b) in C_1}`

  Using this notation, the domain of `f@g` is simply

  `bar(g)^(-1)(bar(f)^(-1)(C)) = (bar(g)^(-1)@bar(f)^(-1))(C)`

  George C. · 1 · Jul 24 2015
• What are some examples of function composition?

  To compose a function is to input one function into the other to form a different function. Here's a few examples.

  Example 1: If `f(x) = 2x + 5` and `g(x) = 4x - 1`, determine `f(g(x))`

  This would mean inputting `g(x)` for `x` inside `f(x)`.

  `f(g(x)) = 2(4x- 1) + 5 = 8x- 2 + 5 = 8x + 3`

  Example 2: If `f(x) = 3x^2 + 12 + 12x` and `g(x) =sqrt(3x)`, determine `g(f(x))` and state the domain

  Put `f(x)` into `g(x)`.

  `g(f(x)) = sqrt(3(3x^2 + 12x + 12))`

  `g(f(x)) = sqrt(9x^2 + 36x + 36)`

  `g(f(x)) = sqrt((3x + 6)^2)`

  `g(f(x)) = |3x + 6|`

  The domain of `f(x)` is `x in RR`. The domain of `g(x)` is `x > 0`. Hence, the domain of `g(f(x))` is `x > 0`.

  **Example 3: if `h(x) = log_2 (3x^2 + 5)` and `m(x) = sqrt(x + 1)`, find the value of `h(m(0))`? **

  Find the composition, and then evaluate at the given point.

  `h(m(x)) = log_2 (3(sqrt(x + 1))^2 + 5)`

  `h(m(x)) = log_2 (3(x + 1) + 5)`

  `h(m(x)) = log_2 (3x + 3 + 5)`

  `h(m(x)) = log_2 (3x + 8)`

  `h(m(2)) = log_2 (3(0) + 8)`

  `h(m(2)) = log_2 8`

  `h(m(2)) = 3`

  Practice exercises

  For the following exercises: `f(x) = 2x + 7, g(x) = 2^(x - 7) and h(x) = 2x^3 - 4`

  a) Determine `f(g(x))`

  b) Determine `h(f(x))`

  c) Determine `g(h(2))`

  Hopefully this helps, and good luck!

  Noah G · 1 · Dec 22 2016

• What is function composition?
• What are some examples of function composition?
• What are some common mistakes students make with function composition?
• Is function composition associative?
• Is it always true that `(f@g)(x) = (g@f)(x)`?
• If `f(x) = x + 3` and `g(x) = 2x - 7`, what is `(f@g)(x)`?
• If `f(x) = x^2` and `g(x) = x + 2`, what is `(f@g)(x)`?
• If `f(x) = x^2` and `g(x) = x + 2`, what is `(g@f)(x)`?
• What is the domain of `(f@g)(x)`?
• What is the domain of the composite function `(g@f)(x)`?
• If `f(x) = x/6 - 2` and `g(x) = 6x + 12`, how can I show `(f@g)(x) = (g@f)(x)`?
• If `f(x) = x^2 + 3x` and `g(x) = 4x - 1`, what is `(f@g)(x)`?
• If `f(x) = x^2 + 3x` and `g(x) = 4x - 1`, what is `(g@f)(x)`?
• If `f(x) = x^2 + 3x` and `g(x) = 4x - 1`, what is `(f@g)(0)`?
• If `f(x) = x^2 + 3x` and `g(x) = 4x - 1`, what is `(g@f)(-3)`?
• How do you write the area a of a circle as a function of its circumference?
• How do you determine `f(g(x))` if `ƒ(x)=x(x + 1)` and `g(x)=x^2−1`?
• If `f(x)=x^2+4x` and `g(x)=3x-5`, how do you find `(f(g(x))` and `g(f(x))`?
• Given `f(x)= x^5+x^3+x`, how do you find the inverse f(3) and f(f inverse (2))?
• If `f(x+1) =2x` and `g(3x) = x+6`, how do you find the value of #f^-1(g(f(13)))3?
• Let `h(x) = x/(x+4)` and `k(x)=2x-4`, how do you find (hºk)(x) and simplify?
• Let `h(t) = (2-t)/(t)` and `g(t)= (3t+15)/t`, how do you find (h/g)(t) and the domain for h/g?
• Let `f(x)=2x+3` and `g(x)=x^2-4` and `h(x)=x-3/2`, how do you find f(g(3))?
• Let `f(x)=2x+3` and `g(x)=x^2-4` and `h(x)=x-3/2`, how do you find g(f(3))?
• Let `f(x)=2x+3` and `g(x)=x^2-4` and `h(x)=x-3/2`, how do you find f(h(x))?
• Let `f(x)=x+2` and `g(x)=sqrtx`, how do you find g(f(x))?
• Let `f(x)= -4x+3` and `g(x)= 1/(x+2)`, how do you evaluate f(g(x)) and g(f(x)) for x?
• Let `u(x)=e^(9x)` and `v(x)=5x+9`, how do you find `(v(u(x)))^2`?
• Let `f(x)=1-x` and `g(x)= x^2` and `h(x)= 1/x`, how do you find `f(g(x))`?
• Let `f(x)=1-x` and `g(x)= x^2` and `h(x)= 1/x`, how do you find g(h(x))?
• Let `f(x)=1-x` and `g(x)= x^2` and `h(x)= 1/x`, how do you find g(f(h(x)))?
• Let `f(x)=1-x` and `g(x)= x^2` and `h(x)= 1/x`, how do you find f(h(g(x)))?
• Let `f(x) = 1 /(x+3)` and `g(x) = -2 /x`, how do you find each of the compositions?
• Let `f(x)= 1/(x-3)`, how do you find f(f(x))?
• Let `f(x)=ln(0.5x)` and `g(x)=e^(3x)`, how do you find each of the compositions?
• Let `f(x) = x^2` and , how do you find each of the compositions?
• Let `g(x) = 3x – 1` and `f(x) = 5x + 2`, how do you find each of the compositions?
• Let `u(x)=2x-1` and `w(x)=x^2`, how do you find u(w(-4)) and w(u(-4))?
• Let `f(x) = 1/x` and `g(x) = sqrt(x-2)`, how do you find each of the compositions and domain and range?
• Let `f(x) = -1 /(x - 7)` and `g(x) = 8-x^2`, how do you find each of the compositions and domain and range?
• Let `f(x)=8x` and `g(x)=x/8`, how do you find each of the compositions and domain and range?
• Let `f(x) = x + 8` and `g(x) = 3x`, how do you find each of the compositions and domain and range?
• Let `f(x) = 1/x^2` and `g(x) = x−1`, how do you find each of the compositions and domain and range?
• Let `F(x)=6-x` and `g(y)=sqrty`, how do you find each of the compositions and domain and range?
• Let `F(x)=3x` and `g(y)=1/y`, how do you find each of the compositions and domain and range?
• Let `h(t) = 1/(t^2)` and `g(t)= sqrt(3t+5)`, how do you find each of the compositions and domain and range?
• Let `F(x)=2/(x-1)` and `G(x)=1/(x+3)`, how do you find each of the compositions and domain and range?
• Let `f(x) = 1 + 2x` and `g(x) = x/(x-1)`, how do you find each of the compositions and domain and range?
• Let `f(x) = 2 -x` and `f(g(x)) = (2x-3)/x`, how do you find g(x)?
• Let `f(x) = (3x -1) /( x - 2 )` and `f(g(x)) =x`, how do you find g(x)?
• Let `f(x) = 4x -3` and `g(f(x)) = 1/(4x)`, how do you find g(x)?
• Let `f(x)=x^2-4` and `g(x)=sqrt(x-3)`, how do you find each of the compositions?
• Let `f(x) = 3/(x-1)` and `g(x) = 2/x`, how do you find each of the compositions?
• Let `f(x)= 1-x^3` and `g(x)= 1/x`, how do you find each of the compositions?
• How do you verify that f(x) and g(x) are inverses: `f(x) = x+7`, `g(x) = x-7`?
• If f(x) = 2x-1 and g(x) = 1/x how do you determine x such that f(g(x)) = g(f(x))?
• How do you solve this function : g[f(x)] if `f(x) = 4x + 1` and `g(x)=2x^2 - 5 = 2x^2 - 5`?
• How do you write `y = (x − 11)^5` as a composition of two simpler functions?
• How do you write `y = 3sqrt(1 + x^2)` as a composition of two simpler functions?
• How do you write `y = 2(x − 3)^5 − 5(x − 3)^2 + 0.5(x − 3) + 11` as a composition of two simpler functions?
• How do you write `y = 1/(x^2 + 3)` as a composition of two simpler functions?
• How do you write `y = sqrt(sqrt(x) + 1)` as a composition of two simpler functions?
• How do you write `y = 2 - sqrt(5 - (3x - 1)^2)` as a composition of two simpler functions?
• Let f(x)=8x-1, and g(x)=x/2 how do you find (fg(x))?
• Let f(x) = 5x + 2 and g(x) = 2x - 1 how do you find (fog)(x)?
• Let f(x) = 8x-1 and g(x) = x/2 how do you find (fog)(x)?
• Let `f(x) =abs(x+1)` and g(x) = 3x-2 how do you find (fog)(x)?
• Let `f(x) =7x+4` and g(x) = x-7 how do you find (fog)(x)?
• Let `f(x) = (1) / (1-3x)` and `g(x) = (1) / (x^2)` how do you find f(g(x)?
• How do you write `h(x) = cos(x^2)` as a composition of two or more functions?
• How do you write `j(x) = sin^2(x)` as a composition of two or more functions?
• How do you write `k(x) = e^sinx` as a composition of two or more functions?
• How do you write `l(x) = (tan(x^2))^.5` as a composition of two or more functions?
• If `f(x)=x^2+1` and `g(x)=x-2`, how do you find f[g(x)]?
• If `f(x)=3x` and `g(x)=4x-3`, how do you find f[g(5)] and g[f(5)]?
• How do you find `f(g(x-3))` if `g(x) = x + 3` and `f(x) = x^2 - 2`?
• How do you find `f(g(x))` if `f(x) = (x-3) / (5x+1)` and `g(x) = (x-1) / (x^2)`?
• How do you find `g(f(x))` if `g(x) = x^2` and `f(x) = x + 3`?
• How do you find `f(g(4))` if `f(x)=2sqrt(x+3)` and `g(x)=-3x+1`?
• How do you find [f • g](x) and [g • f](x) if `F(x)= 2x + 7` and `G(x) = -5x - 1`?
• How do you find [f • g](x) and [g • f](x) if `F(x) = x^2 - 1` and `g(x) = -4x^2`?
• How do you find [f • g](x) and [g • f](x) if `F(x) = x^2 + 2x` and `G(x) = x-9`?
• How do you find (f of g of h) if `f(x)=x^2+1` `g(x)=2x` and `h(x)=x-1`?
• How do you find [g of h](x) if `g(x)=8-2x` and `h(x)=3x`?
• Given the functions `f(x)=x-7` , `g(x)=x^2` and `h(x)=(x-7)^2` how do you find (f+g)(x)?
• Given the functions `f(x)=x-7` , `g(x)=x^2` and `h(x)=(x-7)^2` how do you find (g-f)(x) ?
• Given the functions `f(x)=x-7` , `g(x)=x^2` and `h(x)=(x-7)^2` how do you find (f*g)(x)?
• Given the functions `f(x)=x-7` , `g(x)=x^2` and `h(x)=(x-7)^2` how do you find (f/g)(x)?
• Given the functions `f(x)=x-7` , `g(x)=x^2` and `h(x)=(x-7)^2` how do you find g(f(x))?
• Given the functions `f(x)=x-7` , `g(x)=x^2` and `h(x)=(x-7)^2` how do you find h(g(x))?
• Given the functions `g(x) = 3/(x - 1)`, `f(x) = (x - 1)/(x - 3)` what is g(f(x))?
• Given the functions `f(x) = x^2` and `g(x) = 3x+2` what is f(g(x))?
• Given the functions `g(x) = (2x) (1/2)`, `f(x) = x^2 + 1` what is f(g(x))?
• Given the functions `F(x)=x+4` and `G(x)=2x^2+4` what is f(g(x))?
• How do you find the inverse of `p(x)=x^3-3x^2+3x-1`?
• How do you graph the piecewise function `x, if -2 < x < 2`, `2x, if x < -2`, `3x, if x > 2`?
• How do you graph the piecewise function `3x+2 , if x ≠ 1`, `8 , if x = 1`?
• How do you find the domain and range of the piecewise function `y = x^2 if x < 0`, `y = x + 2 if 0 ≤ x ≤ 3`, `y = 4 if x >3`?
• Given the piecewise function `f(x) = {2x + 1,x < -3 and 4x + 1, x ≥ -3}`, how do you evaluate f(-4)?
• Given the piecewise function `f(x) = {2x + 1,x < -3 and 4x + 1, x ≥ -3}`, how do you evaluate f(-3)?
• Given the piecewise function `f(x) = {2x + 1,x < -3 and 4x + 1, x ≥ -3}`, how do you graph it?
• Given the piecewise function `y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4`, how do you find the domain?
• Given the piecewise function `1-x,x<-1`, `(x^2)-x,-1<=x<=6`, `x-7,x>6`, is it continuous at x=-1 and -6?
• Given the piecewise function `f(x)= 3,x<=0`, `2, if x> 0`, how do you evaluate f(2)?
• Given the piecewise function `f(x)= 3,x<=0`, `2, if x> 0`, how do you evaluate f(-4)?
• Given the piecewise function `3-x, x<=2`, `x^2, x >2`, how do you evaluate f(6)?
• Given the piecewise function `3-x, x<=2`, `x^2, x <2`, how do you evaluate f(2)?
• How do you write write `f(x)=|x-4|` as a piecewise function?
• How do you find the inverse of `f(x)=In(3-2x)+3`?
• How do you find the inverse of `f(x)=(2x+1)/x`?
• How do you find the inverse of `f(x) = x^2 +7`?
• How do you find the inverse of `f(x) =(x + 2)^2 - 4`?
• How do you find the inverse of `f(x) =e^(2x-1)`?
• How do you find the inverse of `H(x)=log x`?
• How do you find the inverse of `f(x)= (2x+1)/(x-3)`?
• How do you find the inverse of `f(x)=(7/x)-3`?
• How do you find the inverse of `f(x) = (2x-1)/(x-1)`?
• How do you find the inverse of `y = Arctan(x+pi/2)`?
• How do you find the inverse of `f(x)=(e^x)/x`?
• How do you find the inverse of `f(x) = x / (x + 8)`?
• How do you find the inverse of `f(x) = root5((3 x - 5) / (x - 5))`?
• How do you find the inverse of `f(x) = 4(x + 5)^2 - 6`?
• How do you find the inverse of `f(x)= x^5+x^3+x`?
• How do you find the inverse of `f(x)= absx + 1`?
• How do you find the inverse of `f(x)=3x^4`?
• How do you find the inverse of `f(x)=2-2x^2`?
• How do you find the inverse of `f(x) = x^2 +x`?
• How do you find the inverse of `f(x) = x^2 + x - 2`?
• How do you find the inverse of `f(x)=(2-3x)/4`?
• How do you find the inverse of `f(x) = 1-x^3`?
• How do you find the inverse of `f(x) = 1-x^3`?
• How do you find the inverse of `f(x)=3^(x+2)`?
• How do you find the inverse of `f(x) = 3x + 1`?
• How do you find the inverse of `f(x) = (x - 2) / (x + 2)`?
• How do you find the inverse of `f(x)=(x-4)^2`?
• How do you find the inverse of `y=x^3 +5`?
• How do you find the inverse of `f(x)=x/5+4`?
• How do you find the inverse of `y=x^2+2x-1`?
• How do you find the inverse of `f(x)=2x+3`?
• How do you find the inverse of `f(x)=4x-1`?
• How do you find the inverse of `f(x) = x^2 + 9`?
• How do you find the inverse of `f(x) =(3x + 1) / -x`?
• What is the inverse of `y=6`?
• How do you find the inverse of `y=log(3x-1)`?
• How do you find the inverse of `H(x)=log x`?
• How do you find the inverse of `f(x) = 3log(x-1)`?
• How do you find the inverse of `y=log_2 2x`?
• How do you find the inverse of `y=log_3 (4x)`?
• How do you find the inverse of `f(x)= -log_5 (x-3)`?
• How do you find the inverse of `f(x)=log[x+1]`?
• How do you find the inverse of `y = 2^x`?
• How do you find the inverse of `y=log_8x`?
• How do you find the inverse of `y=e^(x-1)`?
• How do you find the inverse of `y=-log_5(-x)`?
• How do you find the inverse of `f(x)=log(x+7)`?
• How do you find the inverse of `log 2^-x`?
• How do you find the inverse of `f(x) =2x-5`?
• How do you find the inverse of `f(x) =1/x`?
• How do you find the inverse of `f(x) =10^x`?
• How do you find the inverse of `y=log(x+2)`?
• How do you find the inverse of `y=log_8(x+2)`?
• How do you find the inverse of `g(x) =log ((x)/(1-x))`?
• How do you find the inverse of `y = log_5x`?
• How do you find the inverse of `y = 3^x`?
• How do you find the inverse of `y =1/logx`?
• How do you find the inverse of `g(x)= log_3(x+2)-6`?
• How do you find the inverse of `y = -log_4x`?
• How do you find the inverse of `y=log(x+4)`?
• How do you find the inverse of `y=log_6 x+5`?
• How do you find the inverse of `y=log_5 (x+2)`?
• How do you find the inverse of `y=log_4( x/2 +3 )`?
• How do you find the inverse of `log _(1/2) (x+4)=y`?
• How do you find the inverse of `log _ 1.25 (x)=y`?
• How do you find the inverse of `y=log_5(x+4)+1`?
• How do you find the inverse of `y=log( -3x) +2`?
• How do you find the inverse of `f(x)=2^(x+1) -2`?
• How do you find the inverse of `f(x)=2log(x+1)`?
• How do you find the inverse of `y=log_x4`?
• How do you find the inverse of `y=log_2x`?
• How do you find the inverse of `y=log_2(x+4)`?
• How do you find the inverse of `y=log(4x)`?
• How do you find the inverse of `f(x)=log_3(x-4)-2`?
• How do you find the inverse of `f(x)=-(1/3)^x`?
• How do you find the inverse of `f(x) = x/(x+1)`?
• How do you find the inverse of `f(x) =3(2^x)`?
• How do you find the inverse of `y=log_6 x`?
• How do you find the inverse of `f(x)=3^(x-1)-2`?
• How do you find the inverse of `y=10^x`?
• How do you find the inverse of `y=ln(8x + 1)`?
• How do you find the inverse of `f(x)=x+4`?
• How do you find the inverse of `f(x)=e^-x`?
• How do you find the inverse of `f(x) = 200*3^(x/4)`?
• How do you find the inverse of `y=ln(x+2)`?
• How do you find the inverse of `f(x) = 3 ln (x-2)`?
• How do you find the inverse of `f(x) =ln(x^2)`?
• How do you find the inverse of `y = ln x`?
• How do you find the inverse of `f(x) =ln(4x-1)`?
• How do you find the inverse of `f(x)=x/(x+9)`?
• How do you find the inverse of #3^(2x)?
• How do you find the inverse of `f(x) = 5x - 3`?
• How do you find the inverse of `f(x)= x/(x-9)`?
• How do you find the inverse of `y=log_9 x`?
• How do you find the inverse of `y=log_(1/4) x`?
• How do you find the inverse of `y=log_(1/2) x`?
• How do you find the inverse of `y=log_7 49^x`?
• How do you find the inverse of `y=e^x`?
• How do you find the inverse of `f(x)=2-3 log_4(x+1)`?
• How do you find the inverse of `f(x)=7^(2x+7)`?
• How do you find the inverse of `y=ln(x-1)-6`?
• How do you find the inverse of `y=4^x`?
• How do you find the inverse of `f(x) = 4/x`?
• How do you find the inverse of `y = 1/3log(2x+5) - 4`?
• How do you find the inverse of `f(x)= 1- ln(x-2)`?
• How do you find the inverse of `f(x)=ln (3-2x)+3`?
• How do you find the inverse of `y = e^x/(1 + 4 e^x)`?
• How do you find the inverse of `f(x)= (100)/(1+2^-x)`?
• How do you find the inverse of `y = -logx`?
• How do you find the inverse of `y=log(50x)`?
• How do you find the inverse of `f(x)=log(x+15)`?
• How do you find the inverse of `1-ln(x-2)=f(x)`?
• How do you find the inverse of `f(x)=ln(x-1) - ln(2x +1)`?
• How do you find the inverse of `y=ln(3x+1)`?
• How do you find the inverse of `y=log_(6)x`?
• How do you find the inverse of `f(x)=50,000(0.8)^x`?
• How do you find the inverse of `y=log_3 9x`?
• How do you find the inverse of `f(x)= x/(x-9)`?
• How do you find the inverse of `f(x)=2x+ln(x)`?
• How do you find the inverse of `f(x) = 18 + ln(x)`?
• How do you find the inverse of `h(x)=8x`?
• How do you find the inverse of `g(x)=(x-5) / 2`?
• How do you find the inverse of `f(x)=x^7`?
• How do you find the inverse of `f(x)=(x-1)/(x+2)`?
• How do you find the inverse of `f(x)=10x`?
• How do you find the inverse of `f(x) = ln(5x)`?
• How do you find the inverse of `f(x)=(2x-3)/(x+1)`?
• How do you find the inverse of `y = ln(x + 4)`?
• How do you find the inverse of `y =sqrt(x-4)`?
• How do you find the inverse of `y = (e^x)/(1+2e^x)`?
• How do you find the inverse of `f(x) = (2x)/(x-1)`?
• How do you find the inverse of `g(x)=x^3-1`?
• How do you find the inverse of `2x+3=y`?
• How do you find the inverse of `y=e^x/(1+6e^x)`?
• How do you find the inverse of `y=ln(x/(x-1))`?
• How do you find the inverse of `f(x)=(e^x)+1`?
• How do you find the inverse of `f(x) = 2log (3x-12) + 5`?
• How do you find the inverse of `y = log (x/2)`?
• How do you find the inverse of `y = 5x + 20`?
• How do you find the inverse of `y=ln(x+4)`?
• How do you find the inverse of `y=(1/2)^x`?
• How do you find the inverse of `y=(4x+2)/(x-7)`?
• How do you find the inverse of `g(x)= 2x-4`?
• How do you find the inverse of `f(x) = log7^x`?
• How do you find the inverse of `f(x) = 5^x`?
• How do you find the inverse of `f(x) = -log2^x`?
• How do you find the inverse of `f(x) = 5^x`?
• How do you find the inverse of `f(x) = log 2^x`?
• How do you find the inverse of `y = (log_2 x) +2`?
• How do you find the inverse of `f(x)=e^x-1`?
• How do you find the inverse of `f(x)=1/x^2`?
• How do you find the inverse of `f(x) = (1-2x) / (1+x)`?
• How do you find the inverse of `f(x)=3^(x+2)`?
• How do you find the inverse of `y=2(3)^x +1`?
• How do you find the inverse of `y= 2^(1.5x+3)`?
• How do you find the inverse of `y=e^(3x+1)`?
• How do you find the inverse of `y = x^2 + 9`?
• How do you find the inverse of `f(x)= (x+5)^3-7`?
• How do you find the inverse of `y = 3^x`?
• How do you find the inverse of `y=e^(3x)+2`?
• How do you find the inverse of `y=6^(x)+1`?
• How do you find the inverse of `f(x) = e^x - e^-x`?
• How do you find the inverse of `g(x)= log_8(4 x+6)`?
• How do you find the inverse of `y=1/(x-3)`?
• How do you find the inverse of `f(x)=7`?
• How do you find the inverse of `f(x)=(x+2)^2-4`?
• How do you find the inverse of `f(x)=3sqrt(x+2)`?
• How do you find the inverse of `y=log_6x`?
• How do you find the inverse of `y=log_3x`?
• How do you use composition of functions to show that `f(x)=(2+x)/x` and `f^-1(x) = 2/(x-1)` are inverses?
• If `F(x)= x+2` and `G(x)= x/2`, how do you determine if the composition of functions is commutative?
• How do you find the inverse of `f (x) = 1/3 x +2`?
• How do you find (f o g)(x) if `g(x) = (x^2 -16)^(1/2)`, `f(x) = (3 - x)^(1/2)`?
• How do you determine the three functions f, g, and h such that `(f o g o h)(x) = sin^2(x+1)`?
• How do you find the compositions given `f(x) = x/(x^2+1)`, `g (x) = x^2 +1`?
• How do you find g(h(t)) given `g(t) = (t+1)/2`, `h(t) = (t-3)/4`?
• How do you find `(f@g)(x)` given `g(x) = (2x) (1/2)`, `f(x) = x^2 + 1`?
• How do you find f(g(x)), f(f(x)), g(g(x)), g(f(x)) give `f(x) = x^2`, `g(x) = ln(x)`?
• How do you find g[h(x)] and h[g(x)] given `h(x)=2x-1` `g(x)=3x+4`?
• How do you find the (f o g o h) (x) for `f(x)=(x-2)/(2x+1),`g(x)=3x+1`,`h(x)=x^2#?
• How do you find (g o f)(x) given `f(x)= x/(x-2)`, `g(x)=3/x`?
• How do you find (g o f)(x) when `f(x)=2x` and `g(x)=x^3+x^2+1`?
• How do you find s[h(x)] if `s(x) = 2^x` and `h(x) = x^2`?
• How do you find [f o g](2) and [gof](2)] given `f(x)=2x-1`, `g(x)=-3x`?
• How would you show that `f (x) = 7x +3` and `f^-1(x) = (x +3 )/ 7` are inverses of each other?
• How do you find g[f(x)] if `g(x) = x^2` and `f(x) = x + 3`?
• How do you express the following function, f(x) as a composition of two functions f and g given `f(x)=x^2/(x^2+4)`?
• How do you solve this function : g[f(x)] if f(x) = 4x + 1 and `g(x) = 2x^2 - 5`?
• How do you express the following function, f(x) as a composition of two functions f and g `f(x)=x^2/(x^2+4)`?
• Given `f(x) = (3-2x) / (2x+1)` and `f(g(x)) = 7 - 3x` how do you find g(x)?
• Given `f(x) = 3x - 2x`, `g(x) = sqrtx` and `h(x) = 3x^2 + 2` how do you find (g o f)(-2)?
• Given `f(x)=8x-1`, and `g(x)=x/2` how do you find fog(x)?
• How do you find `(fg)(5)+f(4)` when `f(x)=(x^2)+1` and `g(x)=x-4`?
• Given `f(x) = 7x^2 - 5x`, `g(x) = 17x - 4` how do you find (fog)(6)?
• Given `f(x) = -6x + 7`, `g(x) = 3x + 2` how do you find (gof)(x)?
• Given `f(x) = |2x + 1|`, `g(x) = 3x³ -1` how do you find f(g(x))?
• How do you find the composition of function given `f(x)= sqrt (x+8)` and `g(x)= 4x + 1`?
• How do you express the function `h(x)=(x + 3)^6` in the form f o g?
• What is the difference between (fo(goh)(x) and ((fog)oh)(x)?
• Given `f(x)=6/x^2` and `g(x)=x-3`, how do you find g(f(x))?
• How do you write the combined function as a composition of several functions if `f(g(x)) = sqrt (1-x^2) +2`?
• If `f(x)= 1-x^3` and `g(x)= 1/x` how do you find f(g(x))?
• Let `s(x) = x ^2 + 2x + 3x` and #t(x) = sqrt(x+4), how do you find sot(6)?
• How do you find f(g(x)), f(f(x)), g(g(x)), g(f(x)), given `f(x) = x^2` and `g(x) = ln(x)`?
• How do you find (f of g of h) given `f(x)=x^2+1` `g(x)=2x` and `h(x)=x-1`?
• How do you find [g of h](x) given `g(x)=8-2x` and `h(x)=3x`?
• How do you find the function compositions given `f(x)= 2x-3` and `g(x)=3x`?
• How do you find the function compositions given `f(x)= x^2`, `g(x)= 5x`?
• How do you find the function compositions given `g(x)=x^2-2` and `h(x)=sqrt(5-x)`?
• How do you express the function `y=x^2+3` as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)?
• How do you compute (fog) and (gof) if `f(x) = (3x-1) / (2x+5)` and `g(x) =(7x+3) / (3x-1)`?
• How do you compute (fog) and (gof) if `f(x)= x/(x-2)`, `g(x)=3/x`?
• How do you compute (fog) and (gof) if `g(x) = 3x`, `f(x) = x +1`?
• How do you compute (fog) and (gof) if `g(x) = x^2 - 8`, `f(x) = (-x +1)^(1/2)`?
• How do you write the composite function in the form f(g(x)) `y = sin(7x)`?
• How do you find (f o g)(x) and its domain, (g o f)(x) and its domain, (f o g)(-2) and (g o f)(-2) of the following problem `f(x) = 2x + 3`, `g(x) = 3x -1`?
• How do you find `(f @ g)(x)` and its domain, `(g @ f)(x)` and its domain,`(f @ g)(-2)` and `(g @ f)(-2)` of the following problem `f(x) = x+ 2`, `g(x) = 2x^2`?
• How do you find (f o g)(x) and its domain, (g o f)(x) and its domain, (f o g)(-2) and (g o f)(-2) of the following problem `f(x) = x^2 – 1`, `g(x) = x + 1`?
• How do you find the compositions given `f(x) = 5x + 2` and `g(x) = 2x - 1`?
• How do you find the compositions given `f(x)=8x-1` and `g(x)=x/2`?
• How do you find the compositions given `f(x) =x^2 + 2x + 1` and `g(x) = x - 2`?
• How do you find the compositions given `f(x) = |x + 1|` and `g(x) = 3x - 2`?
• How do you find the compositions given `f(x)=7x+4` and `g(x)=x-7`?
• How do you find the compositions given `f(x)=8x` and `g(x)=x/8`?
• How do you find the compositions given `f(x) = x+4/3` and `g(x) = 3x-4`?
• How do you find the compositions given `f(x)+3x-5` and `g(x)= sqrt(x-2)`?
• How do you find the compositions given `f(x) = x/(x + 1)`, `g(x) = x^2 - 1`?
• How do you find the compositions given `f(x)=3x²` and `g(x)=4-5x`?
• How do you find the compositions given `f(x)= sqrt(x-2)` and `g(x)= x^2-1`?
• How do you find the compositions given `g(x)=4x-1` and `h(x)=sqrt(x+3)`?
• How do you find the compositions given `f(x)=4x^2`, `g(x)=-x+3`?
• How do you find the compositions given `g(x) = 3x + 2` and `h(x) = 9x^2 + 12x + 9`?
• How do you find the compositions given `f(x) = 2x + 3` and `h(x) = 2x^2 + 2x + 1`?
• How do you find the compositions given `f(x)=x+2` and `g(x)= sqrtx`?
• How do you find the compositions given `f(x)=-3x+5`, `g(x)=1+2x-x^2`?
• How do you find the compositions given `f(x)=2-x` and `g(x)=2/(5-x)`?
• How do you find the compositions given `f(x)=x^2` and `g(x)=sqrtx`?
• How do you find the compositions given `f(x) = |x - 2`|, `g(x) = sqrtx`?
• How do you find the compositions given `f(x)=x + 5`, `g(x)= 2x`, `h(x)= x-2`?
• How do you find the compositions given `f(x)=x-7` , `g(x)=x^2` and `h(x)=(x-7)^2`?
• How do you find the compositions given `F(x)=x+4` and `g(x)=x^2`?
• How do you find the compositions given `f(x) = 1/(1+x)` and `g(x) = sqrt(x+2)`?
• How do you find the compositions given `f(x)=3x^2-6x+5` and `g(x)=x^2+5x-2`?
• How do you find the compositions given `f(x)= 5/(x-6)` and `g(x) = 4/5x`?
• How do you find the compositions given `f(x)=x^3+2` and `g(x)=root3(x-2)`?
• How do you find the compositions given `g(x) = x^2 + 2` and `f(x) = 2x`?
• How do you find the compositions given `f(x)=sqrt(x-3)`, `g(x)=sqrt(x +3)`?
• How do you find the inverse of `y=4x+7`?
• How do you find the inverse of `y = -(1/3)^x`?
• How do you find the inverse of `f^-1(x)= -2 - 1/(x-1)`?
• How do you find the inverse of `y=2x^(2)-12x`?
• How do you find the inverse of `f(x) = 3x + 1` and is it a function?
• How do you find the inverse of `h(x)=-3x+6` and is it a function?
• How do you find the inverse of `f(x) = | x | - 3` and is it a function?
• How do you find the inverse of `y=4/(x+4)` and is it a function?
• How do you find the inverse of `y=x^2` and is it a function?
• How do you find the inverse of `y=1-6x^3-3` and is it a function?
• How do you find the inverse of `f(x) = (2x-3)/(x+4)` and is it a function?
• How do you find the inverse of `y = 13/x` and is it a function?
• How do you find the inverse of `y = -13/x` and is it a function?
• How do you find the inverse of `y = 2^x` and is it a function?
• How do you find the inverse of `f(x)=sqrt(x+1) + 3` and is it a function?
• How do you find the inverse of `f(x)=4^x` and is it a function?
• How do you find the inverse of `Y=5X-1` and is it a function?
• How do you find the inverse of `e^-x` and is it a function?
• How do you find the inverse of `y = log_5x` and is it a function?
• How do you find the inverse of `g(x) = x^2 + 4x + 3` and is it a function?
• How do you find the inverse of `f(x) = 2x-4` and is it a function?
• How do you find the inverse of `(x + 2)^2 - 4` and is it a function?
• How do you find the inverse of `y=3-7x` and is it a function?
• How do you find the inverse of `f(x)=x^3-2` and is it a function?
• How do you find the inverse of `y = x + 4` and is it a function?
• How do you find the inverse of `f(x)=x^2+2x-5` and is it a function?
• How do you find the inverse of `f(x)= -|x+1|+4` and is it a function?
• How do you find the inverse of `f(x) = 3 ln (x-2)` and is it a function?
• How do you find the inverse of `y=1/x` and is it a function?
• How do you find the inverse of `y=3x^2-2` and is it a function?
• How do you find the inverse of `f(x) = x – 7` and is it a function?
• How do you find the inverse of `f(x) = 3^x` and is it a function?
• How do you find the inverse of `y=x^3 +5` and is it a function?
• How do you find the inverse of `f(x) =2x-5` and is it a function?
• How do you find the inverse of `f(x) =x^3-2` and is it a function?
• How do you find the inverse of `f(x) =1/(4x+7)` and is it a function?
• How do you find the inverse of `f(x) =10^x` and is it a function?
• How do you find the inverse of `f(x) = (x + 2)^2` and is it a function?
• How do you find the inverse of `f(x) = 1/3x +2` and is it a function?
• How do you find the inverse of `(2x+7)/(3x-1)` and is it a function?
• How do you find the inverse of `y= log_2 (x+4)` and is it a function?
• How do you find the inverse of `f(x)=3x-5` and is it a function?
• How do you find the inverse of `f(x) = sqrt (x-2)` and is it a function?
• How do you find the inverse of `f(x)=3x^2-6x+1` and is it a function?
• How do you find the inverse of `y=6x+3` and is it a function?
• How do you find the inverse of `f(x)=2x+3` and is it a function?
• How do you find the inverse of `x^2 +3` and is it a function?
• How do you find the inverse of `y=-3x+1` and is it a function?
• How do you find the inverse of `y=2x-4` and is it a function?
• How do you find the inverse of `f(x)=(x+3)^(1/2) + 2` and is it a function?
• How do you find the inverse of `f(x)=9 x-4` and is it a function?
• How do you find the inverse of `y = x/(x+1)` and is it a function?
• How do you find the inverse of `y=x^(2)-6x+4` and is it a function?
• How do you find the inverse of `y = (x+3)/(x-2)` and is it a function?
• How do you find the inverse of `y=4^x` and is it a function?
• How do you find the inverse of `f(x) = 1 - (1/x)` and is it a function?
• How do you find the inverse of `f(x) = 4/x` and is it a function?
• How do you find the inverse of `f(x)=x^2-2x-8` and is it a function?
• How do you find the inverse of `f(x) = x^3 + 2x` and is it a function?
• How do you find the inverse of `f(x)= 2/(x+1)` and is it a function?
• How do you find the inverse of `y = 3x-9` and is it a function?
• How do you find the inverse of `f(x)= x^3+x` and is it a function?
• How do you find the inverse of `f(x) = (2x-1)/(x-1)` and is it a function?
• How do you find the inverse of `y= -x` and is it a function?
• How do you find the inverse of `y = 2x^2 - 3x +1` and is it a function?
• How do you find the inverse of `arctan(x+3)` and is it a function?
• How do you find the inverse of `f(x)= (1/2)x + 4` and is it a function?
• How do you find the inverse of `h(X)= 5 / (2x + 3)` and is it a function?
• How do you find the inverse of `h(x)= x^2 - 4x + 5` and is it a function?
• How do you find the inverse of `h(x)= x^3 - 3x^2 + 3x - 1` and is it a function?
• How do you find the inverse of `y = 2^(3 - x)` and is it a function?
• How do you find the inverse of `f(x)= 1/3x + 2` and is it a function?
• How do you find the inverse of `y= x^2-2x+1` and is it a function?
• How do you find the inverse of `y=3x^2+x` and is it a function?
• How do you find the inverse of `y=4-x^2+3x` and is it a function?
• How do you find the inverse of `y=((x^2)-4)/x` and is it a function?
• How do you find the inverse of `h(x)=(5x+1)/4` and is it a function?
• How do you find the inverse of `f(x)=x^2 - 1` and is it a function?
• How do you find the inverse of `f(x) = x/(x+1)` and is it a function?
• How do you find the inverse of `y=log_2 2x` and is it a function?
• How do you find the inverse of `y=(x+3)²-5` and is it a function?
• How do you find the inverse of `y=-2(x+3)²+` and is it a function?
• How do you find the inverse of `f(x)=sqrt(3x)` and is it a function?
• How do you find the inverse of `ln(x^2)` and is it a function?
• How do you find the inverse of `ln(8x + 1)` and is it a function?
• How do you find the inverse of `p(x)=x^3-3x^2+3x-1` and is it a function?
• How do you find the inverse of `2x-2` and is it a function?
• How do you find the inverse of `f(x)=(x+2)/(x-1)` and is it a function?
• How do you find the inverse of `x - 2y = 5` and is it a function?
• How do you find the inverse of `g(x)=5x-2` and is it a function?
• How do you find the inverse of `f(x) = x^2 + x` and is it a function?
• How do you find the inverse of `e^(2x )` and is it a function?
• How do you find the inverse of `f(x) = 3x – 6` and is it a function?
• How do you find the inverse of `y=cos x +3` and is it a function?
• How do you find the inverse of `y=sinx` and is it a function?
• How do you find the inverse of `f(x) = x^2 + 2` and is it a function?
• How do you find the inverse of `y = 3^x` and is it a function?
• How do you find the inverse of `f(x) = x^3 + 5` and is it a function?
• How do you find the inverse of `f(x) = (x + 2)^2` and is it a function?
• Given `f(x) = (x-3) / (5x+1)` and `g(x) = (x-1) / (x^2)` how do you find f(g(x))?
• Given `f(x) = sqrt(42-x)` and `g(x) = x^2 - x` how do you find f(g(x)) and what is it's domain?
• Given `if f(x)=x^2-4` and `g(x)=sqrt(x-3)` how do you find f(g(x)) and g(f(x))?
• Given `f(x) = x^2 + 1` and `g(x) = (2x) (1/2)` how do you find f(g(x))?
• Given `f(x)=x+2` and `g(x)=x-2` how do you find f(g(x))?
• Given `f(x)=x^3+2` and `g(x)=root3(x-2)` how do you show they are inverses?
• Given `f(x) = (3x-1 )/( 2x+5)` and `g(x)=( 7x+3 )/( 3x-1)` how do you find f(g(x))?
• Given `f(x)= sqrt (x+8)` and `g(x)= 4x + 1` how do you find f(g(x)) and g(f(x))?
• Let `f(x)=x^2-4` and `g(x)=sqrtx+3`, how do you find f(g(x))?
• Let `f(x)=x^2-4` and `g(x)=sqrtx+3`, how do you find g(f(x))?
• How do you find f(x+h) for the function f(x)= x - 4?
• How do you find f(x+h) for the function `f(x)= x^2 - 2x + 5`?
• How do you find f(x+h) for the function `f(x)= x^3 + x`?
• How do you find 2p(a) + p(a-1) for the function `p(x) = 4x + 1`?
• How do you find 2p(a) + p(a-1) for the function `p(x)= x^2 - 5x + 8`?
• How do you find 2p(a) + p(a - 1) if `p(x) = x^2 + x`?
• For the function `f(x)= 7e^x` how do you find the following function values: f(-1)?
• For the function `f(x)= 7e^x` how do you find the following function values: f(0)?
• For the function `f(x)= 7e^x` how do you find the following function values: f(1)?
• For the function `f(x)= 7e^x` how do you find the following function values: f(3)?
• If `f(x)=x^2 + 2x +3`, then how do you find f(a-1)?
• How many subgroups does the group `(ZZ_5, o+_5)` have ?
• Let `f(x) = 7x^2+5` and g(x) = x-3, how do you find the composite function (f o g)(2)?
• If`""f^2(x)+g^2(x)+h^2(x)<=9` and `u_x=3f(x)+4g(x)+10h(x)`, again `(u_x)_"max"=sqrtn,"where"" "ninN` then what is the value of n?
• Given `y= (x-3)^5 +2`, how do you find f(x) and g(x) so that the function can be described as y=f(g(x))?
• How do you find `f ^-1(x)` given `f(x) = (x+1)/(x+2)` when x ≠ -2?
• How do you find g o f which is g(f(x)) when f(x)=x^2-2 and g(x)=1/(x-2)?
• How do you find `f@g` which is `f(g(x))` when `f(x)=x^2-2` and `g(x)=1/(x-2)`?
• How do you find the inverse of `y = e^x-1/x`?
• If `-f(x) + f(x-1) = 3x` and `f(1)=1000`, what is `f(20)` ?
• If `f(x)=mx-2` , `g(x)=(3x+2n)/6` and `(g@f)(x)` is a unit function, what is `m+n` ?
• How do you find `(fog)(x)` given `f(x)=2x^3-5x^2` and `g(x)=2x-1`?
• How would you find `f^-1` and verify that `f(f^-1(x))=f^-1(f(x))=x`, if `f(x)=2x+3`? `f(x)=x^3+1`?
• Given that `f(x)=x^2-4x` and `g(x)=x+3`, what is `(f∘g)(1)`?
• Question #6c5fe
• How does this simpify?
• The two functions t(x) and v(x) are defined below. t(x)=6x-1 v(x)=x^2+2 Evaluate the composition of functions v(t(4))?
• F(x)=1/2x; g(x)=1/3x find f(g(x) and g(f(x) State domain of each Precalculus questions?
• What is the difference between x-intercepts, zeros, and roots?
• Let `f(x)=x^2-12` and `g(x)=15-x`, how do you find `(f/g)(5)`?
• How do I find the inverse of `f(x)=(x+3)/(x-2)`?
• How do I find the inverse of `f(x)=(x-5)^2`?
• What is the domain of `fog(x)` given `f(x)=sqrt(x-2)` and `g(x)=1/(2x)`?
• How do you find the inverse of each function `y=x^2-12`?
• If `f(x)=-2x+7` and `g(x)=x+2`, what is `f * g`?
• If `f(x)=-2x+11` and `g(x)=x-6`, how do you find `[fog](x)` and `[gof](x)`?
• If `g(x)=-2x^2-5x` and `h(x)=3x+2`, how do you find `g(h(x))`?
• If `f(x)=x+3` how do you find the inverse?
• If `f(x)=x^2-3` and `g(x)=5x`, how do you find f(g(-3))?
• If `g(x)=x^2+5x+4` and `f(x)=x-2`, how do you find g(f(-2))?
• How do you evaluate `f(-3)` given `f(x)=4x^3+x^2-5x`?
• How do you evaluate `g(m+1)` if `g(x)=2x^2-4x+2`?
• How do you evaluate `f(3)` given `f(x)=2x+3`?
• How do you evaluate `g(-2)` if `g(x)=5x^2+3x-2`?
• How do you evaluate `h(0.5)` if `h(x)=1/x`?
• How do you evaluate `j(2a)` if `j(x)=1-4x^3`?
• How do you evaluate `f(n-1)` if `f(x)=2x^2-x+9`?
• How do you evaluate `g(b^2+1)` if `g(x)=(3-x)/(5+x)`?
• How do you evaluate `f(5m)` if `f(x)=abs(x^2-13)`?
• How do you write two functions for which `(f*g)(x)=2x^2+11x-6`?
• Given `f(x)=3x^2+4x-5` and `g(x)=2x+9`, how do you find `f(x)+g(x)`, `f(x)-g(x)` and `f(x)*g(x)` and `(f/g)(x)`?
• How do you find `[fog](x)` and `[gof](x)` given `f(x)=2x+5` and `g(x)=3+x`?
• How do you find `[fog](x)` and `[gof](x)` given `f(x)=2x-3` and `g(x)=x^2-2x`?
• How do you find `[fog](x)` and `[gof](x)` given `f(x)=x^2-9` and `g(x)=x+4`?
• How do you find `[fog](x)` and `[gof](x)` given `f(x)=1/2x-7` and `g(x)=x+6`?
• How do you find `[fog](x)` and `[gof](x)` given `f(x)=x-4` and `g(x)=3x^2`?
• How do you find `[fog](x)` and `[gof](x)` given `f(x)=x^2-1` and `g(x)=5x^2`?
• How do you find `[fog](x)` and `[gof](x)` given `f(x)=2x` and `g(x)=x^3+x^2+1`?
• How do you find `[fog](x)` and `[gof](x)` given `f(x)=1+x` and `g(x)=x^2+5x+6`?
• How do you find `f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)` given `f(x)=x^2-2x` and `g(x)=x+9`?
• How do you find `f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)` given `f(x)=3/(x-7)` and `g(x)=x^2+5x`?
• How do you find `f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)` given `f(x)=x+3` and `g(x)=(2x)/(x-5)`?
• How do you find the domain of `[fog](x)` given `f(x)=5x` and `g(x)=x^3`?
• How do you find the domain of `[fog](x)` given `f(x)=1/x` and `g(x)=7-x`?
• How do you find the domain of `[fog](x)` given `f(x)=sqrt(x-2)` and `g(x)=1/(4x)`?
• How do you find `f(n-1)` if `f(x)=2x^2-x+9`?
• How do you find (f og)(x) and (g of)(x) given `f(x)=9x-5` and `g(x)=9-3x`?
• If f(x) = 2x + 1 and g(f(x)) = 4x^2 + 4x + 3 , find g(x), given that g(x) is in the form of ax^2 + bx + c. How?
• If `g(0) = 0`, `f'(0) = 2`, `f(0) = 4` and `g'(0) = 3`, then what is the value of `(f @ g)'(0)`?
• For `f(x)= x -3` and `g(x)= x^ 2+4`, how do you find f(g(x)) and g(f(x)) and state the range?
• How do you find the inverse of `y=x^2+12x`?
• Question #90e8c
• How do you find the inverse of `f(x)=4x +7`?
• How do you find the inverse of each of `y=2x-5` and graph them. Draw and label the line of symmetry for the inverse and the original graph?
• Given `f(x)=3x-1, g(x)=x^2-7, h(x)=x^4`, how do you find `(fog)(3)`?
• Given `f(x)=3x-1, g(x)=x^2-7, h(x)=x^4`, how do you find `(goh)(x)`?
• Given `f(x)=3x-1, g(x)=x^2-7, h(x)=x^4`, how do you find `f(g(h(x))`?
• Is the statement true: the graph of `f^-1` is obtained by reflecting the graph of the function f about the line y=x?
• How do you find the inverse of `f(x)=(x-4)/(33-x)`?
• What is the inverse of the function `f(x)=19/x^3`?
• If `f(x)=2x-5` and `g(x)=x^2+1`, what is g(f(x))?
• Let `f(x)=x^2` and `g(x)=sqrtx`, how do you find the domain and rules of `(f*g)(x)`?
• Let `f(x)=x^2` and `g(x)=sqrtx`, how do you find the domain and rules of `(f/g)(x)`?
• Let `f(x)=x^2` and `g(x)=sqrtx`, how do you find the domain and rules of `(f@g)(x)`?
• How do you determine the equation for the inverse of the function `y=2/3x^5`?
• If `f(x)=2x^2- 4x -3` and `g(x)= 2x^2- 16` how do you find f(x)+ g(x)?
• If `f(x)=x^2-81` and `g(x)=(x-9)^-1(x+9)`, how do you find `g(x)timesf(x)`?
• How do you prove that f(x) and g(x) are inverses of each other?
• For `f(x)=x/(x+1)` and `g(x)=9/x`, how do you find `(fog)(x)`?
• Given that f is even function and g is odd function, how do you determine whether h is even or odd or neither `h(x)=2f(x)+xg(x)`?
• How do you determine whether `f(x)=x^5-x` is even, odd, or neither?
• Given that `f(x)=sqrtx` and `g(x)=4x+2`, how do you find `(fog)(x)`?
• Given that `f(x)=sqrtx` and `g(x)=4x+2`, how do you find `(gof)(x)`?
• If `g(x)=2x+1`, how do you find `g(g(x))`?
• How do you find `(fog)(x)` given `f(x)=x^2+3; g(x)=6x`?
• How do you find `f(g(4))` given `f(x)=(x-2)^2; g(x)=x+3`?
• How do you find the inverse of `f(x)=6x`?
• How do you find the inverse of `f(x)=1/3x`?
• How do you find the inverse of `f(x)=3x+1`?
• How do you find the inverse of `f(x)=(x-1)/5`?
• How do you find the inverse of `f(x)=root3x`?
• How do you find the inverse of `f(x)=x^5`?
• How do you show that `f(x)=2x` and `g(x)=x/2` are inverse functions algebraically and graphically?
• How do you show that `f(x)=x-5` and `g(x)=x+5` are inverse functions algebraically and graphically?
• How do you show that `f(x)=7x+1` and `g(x)=(x-1)/7` are inverse functions algebraically and graphically?
• How do you show that `f(x)=3-4x` and `g(x)=(3-x)/4` are inverse functions algebraically and graphically?
• How do you show that `f(x)=x^3/8` and `g(x)=root3(8x)` are inverse functions algebraically and graphically?
• How do you show that `f(x)=1/x` and `g(x)=1/x` are inverse functions algebraically and graphically?
• How do you show that `f(x)=sqrt(x-4)` and `g(x)=x^2+4` are inverse functions algebraically and graphically?
• How do you show that `f(x)=1-x^3` and `g(x)=root3(1-x)` are inverse functions algebraically and graphically?
• How do you show that `f(x)=9-x^2` and `g(x)=sqrt(9-x)` are inverse functions algebraically and graphically?
• How do you show that `f(x)=1/(1+x)` and `g(x)=(1-x)/x` are inverse functions algebraically and graphically?
• How do you show that `f(x)=(x-1)/(x+5)` and `g(x)=-(5x+1)/(x-1)` are inverse functions algebraically and graphically?
• How do you show that `f(x)=(x+3)/(x-2)` and `g(x)=(2x+3)/(x-1)` are inverse functions algebraically and graphically?
• How do you use the horizontal line test to determine whether the function `g(x)=(4-x)/6` is one to one?
• How do you use the horizontal line test to determine whether the function `g(x)=10` is one to one?
• How do you use the horizontal line test to determine whether the function `g(x)=abs(x+4)-abs(x-4)` is one to one?
• How do you use the horizontal line test to determine whether the function `g(x)=(x+5)^3` is one to one?
• How do you use the horizontal line test to determine whether the function `f(x)=1/8(x+2)^2-1` is one to one?
• How do you find the inverse of `f(x)=2x-3` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=3x+1` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=x^5-2` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=x^3+1` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=sqrtx` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=x^2` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=x^2-2` from `x<=0` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=4/x` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=-2/x` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=(x+1)/(x-2)` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=(x-3)/(x+2)` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=root3(x-1)` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=x^(3/5)` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=(6x+4)/(4x+5)` and graph both f and `f^-1`?
• How do you find the inverse of `f(x)=(8x-4)/(2x+6)` and graph both f and `f^-1`?
• How do you determine whether the function `f(x)=x^4` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `f(x)=1/x^2` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `g(x)=x/8` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `f(x)=3x+5` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `p(x)=-4` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `f(x)=(3x+4)/5` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `q(x)=(x-5)^2` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `h(x)=-4/x^2` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `f(x)=sqrt(2x+3)` has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function `f(x)=sqrt(x-2)` has an inverse and if it does, how do you find the inverse function?
• Given `f(x)=1/8x-3` and `g(x)=x^3`, how do you find `(f^-1og^-1)(1)`?
• Given `f(x)=1/8x-3` and `g(x)=x^3`, how do you find `(g^-1of^-1)(-3)`?
• Given `f(x)=1/8x-3` and `g(x)=x^3`, how do you find `(f^-1of^-1)(6)`?
• Given `f(x)=1/8x-3` and `g(x)=x^3`, how do you find `(g^-1og^-1)(-4)`?
• Given `f(x)=1/8x-3` and `g(x)=x^3`, how do you find `(fog)^-1`?
• If `f(x)=x^(1/2)-x` and `g(x)=2x^3-x^(1/2)-x`, how do you find `f(x)-g(x)`?
• How do you find `h(x)=f(x)+g(x)` given `f(x)=abs(x-3)` and `g(x)=4`?
• How do you find `h(x)=f(x)+g(x)` given `f(x)=3x-5` and `g(x)=-x+2`?
• How do you find `h(x)=f(x)+g(x)` given `f(x)=-x-5` and `g(x)=(x+3)^2`?
• How do you find `h(x)=f(x)-g(x)` given `f(x)=6x` and `g(x)=x-2`?
• How do you find `h(x)=f(x)-g(x)` given `f(x)=6-x` and `g(x)=(x+1)^2-2`?
• How do you find `h(x)=f(x)-g(x)` given `f(x)=cosx` and `g(x)=4`?
• Given `f(x)=3x^2+2, g(x)=sqrt(x+4), h(x)=4x-2` how do you determine the combined function `y=(h-g)(x)` and state its function?
• Given `f(x)=3x^2+2, g(x)=sqrt(x+4), h(x)=4x-2` how do you determine the combined function `y=(g-h)(x)` and state its function?
• Given `f(x)=2^x, g(x)=4` how do you determine the combined function `y=(f-g)(x)` and state its function?
• Given `f(x)=3x^2+2, g(x)=4x, h(x)=7x-1`, how do you determine the combined function of `y=f(x)+g(x)+h(x)`?
• Given `f(x)=3x^2+2, g(x)=4x, h(x)=7x-1`, how do you determine the combined function of `y=f(x)+g(x)-h(x)`?
• Given `f(x)=3x^2+2, g(x)=4x, h(x)=7x-1`, how do you determine the combined function of `y=f(x)-g(x)+h(x)`?
• Given `f(x)=3x^2+2, g(x)=4x, h(x)=7x-1`, how do you determine the combined function of `y=f(x)-g(x)-h(x)`?
• If `h(x)=(f+g)(x), f(x)=5x+2` how do you determine g(x) given `h(x)=x^2+5x+2`?
• If `h(x)=(f+g)(x), f(x)=5x+2` how do you determine g(x) given `h(x)=sqrt(x+7)+5x+2`?
• If `h(x)=(f+g)(x), f(x)=5x+2` how do you determine g(x) given `h(x)=2x+3`?
• If `h(x)=(f+g)(x), f(x)=5x+2` how do you determine g(x) given `h(x)=3x^2+4x-2`?
• If `h(x)=(f-g)(x), f(x)=5x+2` how do you determine g(x) given `h(x)=-x^2+5x+3`?
• If `h(x)=(f-g)(x), f(x)=5x+2` how do you determine g(x) given `h(x)=sqrt(x-4)+5x+2`?
• If `h(x)=(f-g)(x), f(x)=5x+2` how do you determine g(x) given `h(x)=-3x+11`?
• How do you determine `h(x)=f(x)g(x)` and `k(x)=f(x)/g(x)` given `f(x)=x+7` and `g(x)=x-7`?
• How do you determine `h(x)=f(x)g(x)` and `k(x)=f(x)/g(x)` given `f(x)=2x-1` and `g(x)=3x+4`?
• How do you determine `h(x)=f(x)g(x)` and `k(x)=f(x)/g(x)` given `f(x)=sqrt(x+5)` and `g(x)=x+2`?
• How do you determine `h(x)=f(x)g(x)` and `k(x)=f(x)/g(x)` given `f(x)=sqrt(x-1)` and `g(x)=sqrt(6-x)`?
• Given `f(x)=x+2, g(x)=x-3, h(x)=x+4` how do you determine `y=f(x)g(x)h(x)`?
• Given `f(x)=x+2, g(x)=x-3, h(x)=x+4` how do you determine `y=(f(x)g(x))/(h(x))`?
• Given `f(x)=x+2, g(x)=x-3, h(x)=x+4` how do you determine `y=(f(x)+g(x))/(h(x))`?
• Given `f(x)=x+2, g(x)=x-3, h(x)=x+4` how do you determine `y=(f(x))/(h(x))times(g(x))/(h(x))`?
• If `h(x)=f(x)g(x)` and `f(x)=2x+5`, how do you determine g(x) given `h(x)=6x+15`?
• If `h(x)=f(x)g(x)` and `f(x)=2x+5`, how do you determine g(x) given `h(x)=-2x^2-5x`?
• If `h(x)=f(x)g(x)` and `f(x)=2x+5`, how do you determine g(x) given `h(x)=2xsqrtx+5sqrtx`?
• If `h(x)=(f(x))/(g(x))` and `f(x)=3x-1`, how do you determine g(x) given `h(x)=(3x-1)/(x+7)`?
• If `h(x)=(f(x))/(g(x))` and `f(x)=3x-1`, how do you determine g(x) given `h(x)=(3x-1)/sqrt(x+6)`?
• If `h(x)=(f(x))/(g(x))` and `f(x)=3x-1`, how do you determine g(x) given `h(x)=1/(x+9)`?
• Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate f(g(3))?
• Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate f(g(2))?
• Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate g(f(2))?
• Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate g(f(3))?
• If `f(x)=2x+8` and `g(x)=3x-2`, how do you find `f(g(1))`?
• If `f(x)=2x+8` and `g(x)=3x-2`, how do you find `f(g(-2))`?
• If `f(x)=2x+8` and `g(x)=3x-2`, how do you find `g(f(-4))`?
• If `f(x)=2x+8` and `g(x)=3x-2`, how do you find `g(f(1))`?
• If `f(x)=3x+4` and `g(x)=x^2-1`, how do you find `f(g(a))`?
• If `f(x)=3x+4` and `g(x)=x^2-1`, how do you find `f(g(x))`?
• If `f(x)=3x+4` and `g(x)=x^2-1`, how do you find `g(f(x))`?
• If `f(x)=3x+4` and `g(x)=x^2-1`, how do you find `g(g(x))`?
• How do you determine `f(g(x))` and `g(g(x))`, given `f(x)=x^2+x` and `g(x)=x^2+x`?
• How do you determine `f(g(x))` and `g(g(x))`, given `f(x)=sqrt(x^2+2)` and `g(x)=x^2`?
• How do you determine `f(g(x))` and `g(g(x))`, given `f(x)=absx` and `g(x)=x^2`?
• Given `f(x)=sqrtx` and `g(x)=x-1`, how do you determine the domain and range of `y=f(g(x))`?
• If `h(x)=(fog)(x)`, how do you determine `h(x)=(2x-5)^2` and `f(x)=x^2`?
• Let `j(x)=x^2` and `k(x)=x^3`, does `k(j(x))=j(k(x))`?
• If `s(x)=x^2+1` and `t(x)=x-3`, does `s(t(x))=t(s(x))`?
• If `h(x)=f(g(x))` how do you determine f(x) and g(x) given `h(x)=2x^2-1`?
• If `h(x)=f(g(x))` how do you determine f(x) and g(x) given `h(x)=abs(x^2-4x+5)`?
• If `f(x)=1/(1+x)` and `g(x)=1/(2+x)` how do you determine f(g(x))?
• Let `f(x)=(x+3)^2` and `g(x)=x+4`, how do you find `h(x)=f(x)+g(x)`?
• Let `f(x)=x+8` and `g(x)=2x^2-128`, how do you find `h(x)=(g(x))/(f(x))`?
• Given `f(x)=5-x` and `g(x)=2sqrt(3x)` what is the value of `f(g(3))`?
• What is `y=f(g(x))` if `f(x)=x+5` and `g(x)=x^2`?
• What is `y=f(g(x))` if `f(x)=4^x` and `g(x)=x+1`?
• What is `y=f(g(x))` if `f(x)=x^4` and `g(x)=sqrtx`?
• Given `f(x)=2x^2+11x-21` and `g(x)=2x-3` how do you determine `y=f(x)-g(x)`?
• Given `f(x)=2x^2+11x-21` and `g(x)=2x-3` how do you determine `y=(f(x))/(g(x))`?
• Given `f(x)=2x^2+11x-21` and `g(x)=2x-3` how do you determine `y=f(g(x))`?
• Question #7ca7c
• Question #dfc1c
• How do you find the inverse of the function `f(x)=1/2x+10`?
• Question #37dc6
• Question #9ff05
• If `h(x)=2x-6` and `h(g(x))=2-2x`, find `g(x)`?
• Question #9e4a8
• Question #7adc3
• How do you find the equation for the inverse of `y=2x+1`?
• How do you find the equation for the inverse of `y=1/3x`?
• How do you find the equation for the inverse of `y=6x-3`?
• How do you find the equation for the inverse of `y=-4x+6`?
• How do you find the equation for the inverse of `y=x^2+2, x>=0`?
• How do you verify if `f(x)=x+4; g(x)=x-4` are inverse functions?
• How do you verify if `f(x)=7x; g(x)=1/7x` are inverse functions?
• How do you verify if `f(x)=x^5; g(x)root5x` are inverse functions?
• How do you verify if `f(x)=2x-4; g(x)=1/2x+2` are inverse functions?
• How do you verify if `f(x)=3-x; g(x)=3-x` are inverse functions?
• How do you verify if `f(x)=x^2+5; x>=0; g(x)=sqrt(x-5)` are inverse functions?
• How do you graph `f(x)=2x+1` and then use the horizontal test to determine whether the inverse of f is a function?
• How do you graph `f(x)=-x-2` and then use the horizontal test to determine whether the inverse of f is a function?
• How do you graph `f(x)=-x^2+3, x>=0` and then use the horizontal test to determine whether the inverse of f is a function?
• How do you graph `f(x)=1/4x^3` and then use the horizontal test to determine whether the inverse of f is a function?
• How do you graph `f(x)=3/x` and then use the horizontal test to determine whether the inverse of f is a function?
• How do you verify that `f(x)=3x+5; g(x)=1/3x-5/3` are inverses?
• How do you verify that `f(x)=-2x-3; g(x)=-1/2x-3/2` are inverses?
• How do you verify that `f(x)=x^2+2, x>=0; g(x)=sqrt(x-2)` are inverses?
• How do you verify that `f(x)=1/3x^3-2; g(x)=root3(3x+6)` are inverses?
• How do you verify that `f(x)=3x^4+1, x>=0; g(x)=root4(1/3x-1/3)` are inverses?
• How do you verify that `f(x)=(3-x)/x; g(x)=3/(x+1)` are inverses?
• How do you find the inverse of `f(x)=3-2x`?
• How do you find the inverse of `f(x)=1/5x+3`?
• How do you find the inverse of `f(x)=sqrt(x-3)`?
• How do you find the inverse of `f(x)=sqrt(2x+5)`?
• How do you find the inverse of `f(x)=4x^7`?
• How do you find the inverse of `f(x)=4x^2+1, x>=0`?
• How do you find the inverse of `f(x)=(4-x)/(3x)`?
• How do you find the inverse of `f(x)=root5(5x+4)`?
• How do you find the inverse of `f(x)=1/(2x)`?
• How do you graph the function `f(x)=-x^3+1` and then use the horizontal line test to determine whether the inverse of f is function?
• How do you graph the function `f(x)=(x+3)(x-1)` and then use the horizontal line test to determine whether the inverse of f is function?
• Relationship of Input and Output values of Composite Functions. How would you evaluate f(g(x)?
• What is the inverse function of `f(x) = 2log_4 x`?
• How do you solve this function? When x=(a+2).
• Question #d780a
• Question #da9aa
• If `f(x)=sqrtx`, `g(x)=7x+b` and `f(g(x))` passes through `(4,6)`, what is `b`?
• (k o h)? `k(x) = 1/x, h(x) = x^2 + 1` Find the indicated functions.
• (k o g)? k(x) = 1/x, g(x) = 2x^2 + 4x Find the indicated functions.
• Question #86e50
• Question #43f3b
• Question #55f42
• Let `f(x)=x^2+5` and `g(x)= (x+5)/x`. What is `(g*f)(-3)`?
• If `f(x) = sqrt(x+8)` and `g(x) = sqrt(x+7)`, what is `(f+g)(x)`?
• Find the function composition `f@g(x)=f(g(x))` where `f(x ) = 8x-18` and `g(x) = 1/2x-1`?
• Given that `f(x)=x+2` and `g( f(x) ) = x^2 + 4x-2` then write down `g(f(x))`?
• What is the composition form f(g(x)) for the following Chain Rule function, where the inner function u=g(x), and the outside y = f(u)?
• Let f(x)=`x^2+2` and g(x)=2x−2, evaluate: f(g(3))?
• Let f(x) = 2x − 5and g(x) = 5x − 2. what is (g ∘ f)(−6)?
• Let f(x) = 2x − 3and g(x) = 3x − 2. what is (f ∘ g)(−2)?
• Let f(x) = x2 − 9 and g(x) = 3x − 4. what is (f · g)(−3)?