Answer
Discontinuities at $ x=1$ (nonremovable) and $ x=2$ (removable).
Work Step by Step
We are given the function $ f(x)$. The discontinuity at $ x=1$ is a jump discontinuity and therefore cannot be removed. The discontinuity at $ x=2$ can be removed by defining $ f(2)=1$ (that would make the limit as $ x $ goes to $2$ equal to $ f(2)$, since the limit exists).