Answer
See below.
Work Step by Step
We know that if a function is odd, then $f(-x)=-f(x).$ So here $f(-x)=-f(x)$. We know that if a function is even, then $f(-x)=f(x).$ So here $g(-x)=g(x)$.
Then $f(g(-x))=f(g(x))=$, thus $f(g(x))$ is even and $g(f(-x))=g(-f(x))=g(f(x))$, thus $g(f(x))$ is even Thus we proved what we had to.
