Answer
$ f $ is discontinuous at $x=-1$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
$\lim_\limits{x\to -1} f(x)=\lim_\limits{x\to -1} \dfrac{x^2-1}{x+1}$
$\lim_\limits{x\to -1} f(x)=\lim_\limits{x\to -1} \dfrac{(x-1)(x+1)}{x+1}=\lim_\limits{x\to -1} (x-1)$
$\lim_\limits{x\to -1} f(x)=(-1) -(1)=-2$
and $ f(-1) =6$
So, $\lim_\limits{x\to -1} f(x) \neq f(-1)$
Therefore, the function $ f $ is discontinuous at $x=-1$
