Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

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

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

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

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