Determine whether the functions are odd, even, or neither without using graphs

Question

Determine whether the following functions are odd, even, or neither:

$y=10(e^x+e^{-x})$

$y=e^{-x} \cos(2x)$

$y=x^8\sin (2x)$

Answer 1

Hints:

An even function is one such that $f(-x) = f(x)$.

An odd function is one such that $f(-x) = -f(x)$.

Also:

$$\cos(-x) = \cos(x)$$ $$\sin(-x) = -\sin(x)$$

These will get you most of the way there. Really all you need to do is evaluate the function at $-x$ and see what happens. Hopefully this helps, but if you provide more detail in the OP about where you are getting stuck or confused, then it's much easier for us help you.