1. ## Function Proof

Question: Prove that the product of two odd functions is an even function.

I know a few basic facts about even and odd functions:

In an even function, e(x)=e(-x)
In an odd function, o(-x)=-o(x)
An even function is a reflection across the y-axis.
An odd function is a reflection across the origin.

where e and o are even and odd functions respectively.

How would I go about using this knowledge, and possibly other information, to complete this proof? Any suggestions are appreciated.

2. let $f(x)$ and $g(x)$ both be odd functions.

Then $f(-x)g(-x) = -f(x)*-g(x) = f(x)g(x)$

3. Thanks! I get it now.