Question

Is the product of an odd function and an even function odd or even?

Answer 1

odd

Explanation:

Suppose `f(x)` is odd and `g(x)` is even.

Then `f(-x) = -f(x)` and `g(-x) = g(x)` for all `x`

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

Then:

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

for all `x`

That is `h(x)` is odd.