Answer
See the explanation below.
Work Step by Step
$f$ can not be a closed function, because closed functions are continuous on their DOMAINS.
Since the domain is $\mathbb{R}$, a closed function $f$ is continuous at $x=2$.
Thus, the function must not be closed, but rather it must be piecewise.
For example, $f(x)=\left\{\begin{array}{lll}
-1, & for & x\lt 2\\
+1 & for & x \geq 2
\end{array}\right.$
is defined on all of $\mathbb{R}$, but the one-sided limits at $x=2$ differ, which means that no limit exists there.
Thus, $f$ is discontinuous at $x=2$.
