Which of the following is a function that has a jump discontinuity at $x=2$ and a removable discontinuity at $x=4$, but is continuous elsewhere?

(a) $f(x)= \displaystyle \frac{2}{(x-2)(x-4)}$.

(b) $f(x) = \begin{cases} 1 & \textrm{if }x \leq 2 \\ x-3 & \textrm{if }2 < x < 4\textrm{ or }x > 4 \\ 3 & \textrm{if }x = 4 \\ \end{cases}$.

(c) $f(x) = \begin{cases} 2-x^2 & \textrm{if }x \leq 2 \\ \displaystyle \frac{1}{x^2-4x} & \textrm{if }x > 2\\ \end{cases}$.