According to defintion of compostion of functions, we can get:
\((f\circ g)(x)=f(g(x))\)
But we know, that:
\(\displaystyle h(x)= \frac{x^2}{x^2+4}\)
Our goal, is to express that function as a composition:
\((f\circ g)(x)=h(x) \Rightarrow f(g(x))=h(x)\)
I.e:
\(\displaystyle f(g(x))=\frac{x^2}{x^2+4}\)
If \(\displaystyle f(y)= \frac{y}{y+4}\) then \(g(x)=x^2\). Hence, \(\displaystyle h(x)=(f\circ g)(x)=f(g(x))= \frac{g(x)}{g(x)+4} \Rightarrow f(g(x))=f(x^2)= \frac{x^2}{x^2+4}\)