Question

Given the definitions of f(x) and g(x) below, find the value of (gof)(3).

f(x) = 2x² - x - 15
g(x) = -5x +9

Answer 1

`\huge{ \boxed{gof(3) = 9}}`

Explanation:

In order to find gof(3), we first have to find gof(x). To find gof(x) substitute the f(x) into g(x). That is, for every x found in g(x) substitute it by f(x).

From the question

`f(x) = 2 {x}^(2) - x - 15 \\ g(x) = - 5x + 9 \\ \\ gof(x) = - 5(2 {x}^(2) - x - 15) + 9 \\ gof(x) = - {10x}^(2) + 5x + 75 + 9 \\ \\ gof(x) = - {10x}^(2) + 5x + 84`

To find gof(3), substitute the value of x that is 3 into gof(x). For every x found in gof(x), replace it by 3 and solve.

`gof(3) = - 10( {3})^(2) + 5(3) + 84 \\ \quad \: \: \: \: \: = - 10(9) + 15 + 84 \\ \: \: \: = - 90 + 15 + 84 \\ = 9`

We have the final answer as

gof(3) = 9