Question

PLEASE HELP FOR MATH

Answer 1

Answer:

$f(x) = 3x^2$ and $g(x) = x + 2$

Step-by-step explanation:

Given

$h(x) = 3(x+2)^2$

$h(x) = (fog)(x)$

Required

Find possible expressions for f(x) and g(x)

$h(x) = (fog)(x)$

This can be rewritten as:

$h(x) = f(g(x))$

Recall that $h(x) = 3(x+2)^2$

So;

$h(x) = f(g(x)) = 3(x+2)^2$

$f(g(x)) = 3(x+2)^2$

By comparison, the expression in bracket represents g(x);

Hence;

$g(x) = x + 2$

Replace g(x) with x

$f(x) = 3(x)^2$

$f(x) = 3x^2$

Hence, the possible expressions of f(x) and g(x) are:

$f(x) = 3x^2$ and $g(x) = x + 2$