Question

If h(x) = (fºg)(x) and h(x) = 3(x+2)^2 find one possibility for f (x) and g(x).

Answer 1

Answer:

$f(x) = 3x^2$

$g(x) = x + 2$

Step-by-step explanation:

Given

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

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

Required

Find  f(x) and g(x)

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

Rewrite h(x)

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

If  $h(x) = 3(x+2)^2$

then

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

This implies that; the expression in the brackets are equal;

In other words; function g(x) on the left hand side is equal to expression x + 2 on the right hand side

So;

$g(x) = x + 2$

To find f(x), substitute g(x) with x

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

$f(x) = 3x^2$

Final solutions are

$f(x) = 3x^2$

$g(x) = x + 2$