The title pretty much explains it:
Given that $s(x)$ is even and $t(x)$ is odd, and both are defined on the real line $\mathbb R$, is $s(t(x))$ even or odd?
Some things I found out on my own:
I found that $s(x) t(x)$ is odd because:
$$st(-x) = s(-x) \cdot t(-x)$$
$$st(-x) = s(x) \cdot (-t(x))$$ (This is because for an even function, $f(-x) = f(x)$, and for an odd function, $f(-x) = -f(x)$.)
$$st(-x) = -st(x)$$
Therefore, by definition, $s(x) t(x)$ is odd.
I still can't figure out $s(t(x))$ though...
Any help is appreciated.
Thank you in advanced.