Question

How do you find `(f-g)(3)` given `f(x)=x^2-1 and`g(x)=2x-3`and`h(x)=1-4x#?

Answer 1

Compute `(f-g)(x)` and then evaluate at `x = 3`

OR

Evaluate `f(3)" and "g(3)` and then perform the subtraction.

`(f-g)(3) = f(3)-g(3)`

Explanation:

Compute `(f-g)(x)`:

`(f-g)(x) = f(x) - g(x)`

Substitute the equivalents for `f(x)" and " g(x)`

`(f-g)(x) = x^2-1 - (2x-3)`

Distribute the minus sign:

`(f-g)(x) = x^2-1 -2x+3`

Combine like terms:

`(f-g)(x) = x^2 -2x+2`

Evaluate at `x = 3`:

`(f-g)(3) = 3^2 -2(3)+2`

`(f-g)(3) = 5`

OR

Evaluate `f(x)" at "x=3`:

`f(3) =`3^2 - 1#

`f(3) = 8`

Evaluate `g(x)" at "x=3`

`g(3) = 2(3)-3`

`g(3) = 3`

`(f-g)(3) = f(3)-g(3)`

`(f-g)(3) = 8-3`

`(f-g)(3) = 5`

Either always works.