Question

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

A.
f(x) = x + 2
g(x) = 3x^2
B.
f(X) = (x+2)^2
g(x)=3x^2
C.
f(x)=3x2^2
g(x)= (x+2)^2
D.
f(x) =3x2^2
g(x) = x+2

Answer 1

`f(x) = 3x^2`

`g(x) = x + 2`

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`