Answer
Please see below.
Work Step by Step
As we see the graph of $g(x)=\begin{cases}x^2-3x, & x >4 \\ 2x-5, & x \le 4 \end{cases}$, we find that the function has a discontinuity at $x=4$ because the left- and right-handed limits are different at this point:$$\lim_{x \to 4^-}g(x)=3, \qquad \lim_{x \to 4^+}g(x)=4$$
