At which values of $x_0$ does $\lim\limits_{x \rightarrow x_0} g(x)$ exist?

Question

My answer is $(-\infty , -4) \cup (-4, \infty)$ but I am not sure if my answer is right.

Answer 1

Your answer is absolutely correct.

Answer 2

The function is discontinuous at $x=-4$. All other points it is continuous.