Question

Given the definitions of f(x) and g(x) below, find the value of (gof)(9).

f(x) = -2x + 14
g(x) = 2x2 - 6x – 2

Answer 1

The value of (gof)(9)=54

Explanation:

We are given:

`f(x) = -2x + 14\\g(x) = 2x^2 - 6x - 2`

We need to find (gof)(9).

To find (gof)(9) first we will find g(f(x)) and then put x=9

Finding g(f(x))

By putting value of f(x) into g(x) i.e

`g(f(x))=2(-2x+14)^2-6(-2x+14)-2`

Now putting x=9

`g(f(9))=2(-2(9)+14)^2-6(-2(9)+14)-2\\g(f(9))=2(-18+14)^2-6(-18+14)-2\\g(f(9))=2(-4)^2-6(-4)-2\\g(f(9))=2(16)+24-2\\g(f(9))=32+24-2\\g(f(9))=54`

so, the value of (gof)(9)=54