Question

Given the definitions of f(x) and g(x)

below, find the value of f(g(-4)). F(x)=4x+6 g(x)=x^ 2+x-9

Answer 1

`f(g(-4)) = 18`

Explanation:

Given

`f(x) = 4x + 6`

`g(x) = x^2 + x - 9`

Required

Find f(g(-4))

First, calculate f(g(x))

We have:

`f(x) = 4x + 6`

`f(g(x)) = 4g(x) + 6`

Substitute:
`g(x) = x^2 + x - 9`

`f(g(x)) = 4[x^2 + x - 9] + 6`

Open bracket

`f(g(x)) = 4x^2 + 4x - 36 + 6`

`f(g(x)) = 4x^2 + 4x-30`

Substitute
`-4` for
`x`

`f(g(-4)) = 4*(-4)^2 + 4*(-4)-30`

`f(g(-4)) = 64 -16 -30`

`f(g(-4)) = 18`