Question

If f(x) is an even function and g(x) is an odd function, how do you prove that h(x) = f(x) * g(x) is odd?

Answer 1

See below

Explanation:

We have `f` is even, `g` is odd and `h=fg`.

So

`f(-x)=f(x)` and `g(-x)=-g(x)`

and

`h(-x)=f(-x)g(-x)=-f(x)g(x)=-h(x)`

so `h` is odd.