This operation is equivalent to:
[tex](f\circ g)(x)=f(g(x))[/tex]
It is like a function inside a function. So, we can look for parts in h(x) that are common and call that the function inside.
As we can see, h(x) have terms with x + 4, so if we call:
[tex]g(x)=x+4[/tex]
We can see that h(x) becomes:
[tex]h(x)=(g(x))^2+2g(x)[/tex]
And if we substitute g(x) by x, we will get the expression of the ouside function f(x):
[tex]f(x)=x^2+2x[/tex]
This way, we have:
[tex](f\circ g)(x)=(g(x))^2+2g(x)=(x+4)^2+2(x+4)=h(x)[/tex]
So, the functions are:
[tex]\begin{gathered} g(x)=x+4 \\ f(x)=x^2+2x \end{gathered}[/tex]
