How do you find the inverse of $f (x) = 2 x + 3$ $f(x)= 2x +3$ ?

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Answer 1 · 2018-03-24T17:09:12

$f^{- 1} (x) = \frac{x - 3}{2}$ $f^-1(x)=(x-3)/2$

$y = f (x)$ $y=f(x)$

$y = 2 x + 3$ $y=2x+3$

Switch the places of $x$ $x$ and $y :$ $y:$

$x = 2 y + 3$ $x=2y+3$

Solve for $y :$ $y:$

$2 y = x - 3$ $2y=x-3$

$y = \frac{x - 3}{2}$ $y=(x-3)/2$

$f^{- 1} (x) = \frac{x - 3}{2}$ $f^-1(x)=(x-3)/2$

Answer 2 · 2018-03-24T17:10:59

$y = \frac{x - 3}{2}$ $y=(x-3)/2$

Now, the inverse of a function is just writing $x$ $x$ in terms of $y$ $y$

So $f (x) = 2 x + 3$ $f(x)=2x+3$ becomes $y = 2 x + 3$ $y=2x+3$

$y = 2 x + 3$ $y=2x+3$ becomes $y - 3 = 2 x$ $y-3=2x$

$y - 3 = 2 x$ $y-3=2x$ becomes $\frac{y - 3}{2} = x$ $(y-3)/2=x$

or $x = \frac{y - 3}{2}$ $x=(y-3)/2$

Finally just interchange x and y because we want the function in terms of x.
$y = \frac{x - 3}{2}$ $y=(x-3)/2$

So $f^{- 1} (x) = \frac{x - 3}{2}$ $f^-1(x)=(x-3)/2$

How do you find the inverse of f(x)=2x+3f(x)= 2x +3?