We are asked to find two functions $f(x)$ and $g(x)$ such that their composition $f(g(x))$ equals $\frac{2}{(x+5)^2}$.

1. Problem Description

We are asked to find two functions $f(x)$ and $g(x)$ such that their composition $f(g(x))$ equals $\frac{2}{(x+5)^2}$.

2. Solution Steps

We want to find functions $f(x)$ and $g(x)$ such that $f(g(x)) = \frac{2}{(x+5)^2}$.

One simple approach is to let $g(x) = x+5$ and $f(x) = \frac{2}{x^2}$. Then,

$f(g(x)) = f(x+5) = \frac{2}{(x+5)^2}$.

Another possible solution would be $g(x)=(x+5)^2$ and $f(x) = \frac{2}{x}$. Then

$f(g(x)) = f((x+5)^2) = \frac{2}{(x+5)^2}$.

There are many possible answers.

3. Final Answer

$f(x) = \frac{2}{x^2}$

$g(x) = x+5$