Answer:
[tex]f(x) = 3x^2[/tex]
[tex]g(x) = x + 2[/tex]
Step-by-step explanation:
Given
[tex]h(x) = 3(x+2)^2[/tex]
[tex]h(x) = (fog)(x)[/tex]
Required
Find f(x) and g(x)
[tex]h(x) = (fog)(x)[/tex]
Rewrite h(x)
[tex]h(x) = f(g(x))[/tex]
If [tex]h(x) = 3(x+2)^2[/tex]
then
[tex]f(g(x)) = 3(x+2)^2[/tex]
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;
[tex]g(x) = x + 2[/tex]
To find f(x), substitute g(x) with x
[tex]f(x) = 3(x)^2[/tex]
[tex]f(x) = 3x^2[/tex]
Final solutions are
[tex]f(x) = 3x^2[/tex]
[tex]g(x) = x + 2[/tex]
