I need to write a proof showing that h(x) is either odd, even, or neither.

Assume h(x) = f(x)*g(x) and f(x) is even and g(x) is odd.

I think the first step would be substituting as follows: h(x)=f(-x)*-g(x) because of the def'n of even and odd functions.

This is where I am stuck and don't know how to proceed.

Any help is appreciated