Answer
The function $f(x)$ is discontinuous at $x=1$,
(a)
$$
f(1) =2
$$ .
(b)
$$
\lim _{x \rightarrow-1^{-}} f(x)=-2
$$
(c)
$$
\lim _{x \rightarrow-1^{+}} f(x)=-2
$$
(d)
Since
$$
\lim _{x \rightarrow-1^{-}} f(x)=\lim _{x \rightarrow-1^{+}} f(x)=-2
$$
then,
$$
\lim _{x \rightarrow-1} f(x)=-2
$$
(e)
$$
\lim _{x \rightarrow-1} f(x) \ne f(1).
$$
Work Step by Step
The function $f(x)$ is discontinuous at $x=1$,
(a)
$$
f(1) =2
$$ .
(b)
$$
\lim _{x \rightarrow-1^{-}} f(x)=-2
$$
(c)
$$
\lim _{x \rightarrow-1^{+}} f(x)=-2
$$
(d)
Since
$$
\lim _{x \rightarrow-1^{-}} f(x)=\lim _{x \rightarrow-1^{+}} f(x)=-2
$$
then,
$$
\lim _{x \rightarrow-1} f(x)=-2
$$
(e)
$$
\lim _{x \rightarrow-1} f(x) \ne f(1).
$$
