I am having some trouble with the concept of continuity and limits when it applies to questions. Here's a simple question I am not sure how to approach:

$\displaystyle \mbox{If} x^4 \leq \mbox{f(x)} \leq x^2$ for $\displaystyle -1 \leq x \leq 1$ and $\displaystyle x^2 \leq \mbox{f(x)} \leq x^4$ for $\displaystyle x<-1 \mbox{or} x>1$, at what points $\displaystyle \mbox{c}$ do you automatically know $\displaystyle \lim_{x\to\mbox{c}}\mbox{f(x)}$?

What are the values of the limits at these points?

What is the correct approach to this question?