A function is even $\iff$ $f(-x) = f(x)$ and odd $\iff f(-x) = -f(x)$.
If I have some function $f$ that is even and some function $g$ that is even, their composition is $f(g(x))$, right?
When I'm trying to find if this function is even or odd, isn't $g(x)$ technically the $x$ here? so, wouldn't I check $f(-g(x))$, or am I misunderstanding something?
Because I feel like I am, since I am getting different answers than I'm supposed to. But I'm not sure why exactly this isn't okay, because $g(x)$ is just the new variable in this case, is it not?