If $-2\leq f(x)\leq 4$ for all real $x$, then which must exist? $\lim_{x\to-2}\frac1{f(x)}$, $\lim_{x\to-2}\frac{f(x)}x$, $\lim_{x\to-2}(|f(x)|-f(x))$
Your solution is fine but, as mentioned in the comments, the function was probably intended to be continuous. In any case, it is a flaw in the question and you have a good point in case you are not awarded the full score.
If $f$ is continuous:
$(1)$ is not true in general (requires $f(-2) \ne 0$).
$(2)$ is always true, with the limit being $-\frac 12 f(-2)$.
$(3)$ is always true but the value of the limit depends on the sign of $f(-2)$.