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Assume that $f$ and $g$ are odd functions defined for all real numbers. 
\begin{enumerate}
    \item What does it mean for a function $f(x)$ to be odd?
    \item Give an example of an odd function, and use the definition to show that it is odd.
    \item Define a new function $h(x) = f(x)g(x)$. Use the definition to show that $h$ is an even function.
    \item Define another function $k(x) = f(g(x)) = (f \circ g)(x)$. Use the definition of an odd function to show that $k$ is odd.
\end{enumerate}
\textbf{Note:} For this problem, you should not put any examples in for $f$ and $g$ when you are trying to show that $h$ is even and $k$ is odd. You need to leave $f$ and $g$ as general (unknown) functions and use the fact that they are even/odd to get the result you want. 

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