How to check if a function is negligible?

Question

Let $\epsilon(x)$ be a negligible function. Let $p$ be a polynomial such that $p(k) \geq 0$ for all $k > 0$.

What can we say about $\epsilon(p(k))$? Is this a negligible function? If yes, then is there any formal or informal way to check whether a given function is negligible?