Question

A) Let f(x) = 4x + 2 and g(x) = 2x^2-4. Find the formula for the composition function gof

(4Marks)​

Answer 1

g o f =
`g(f(x)) = 32x^2 + 32x + 4`

Explanation:

Given

`f(x) = 4x +2`

`g(x) =2x^2 - 4`

Required:

Find g o f

This is calculated as:

`gof = g(f(x))`

`g(x) =2x^2 - 4`

So:

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

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

`g(f(x)) = 2[ 16x^2 + 16x + 4)] - 4`

`g(f(x)) = 32x^2 + 32x + 8 - 4`

`g(f(x)) = 32x^2 + 32x + 4`