Answer
See explanations.
Work Step by Step
Step 1. With the given conditions, we have $f(-x)=-f(x)$ and $g(-x)=g(x)$
Step 2. $f\circ g=f(g(x))$ and $f(g(-x))=f(g(x))$, thus $f\circ g$ is even.
Step 3. $g\circ f=g(f(x))$ and $g(f(-x))=g(-f(x))=g(f(x))$, thus $g\circ f$ is even.
