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.