Answer
Discontinuities are at $ x=0$ (removable) and $ x=1$ (nonremovable).
Work Step by Step
We are given the function $ f(x)$. The function $ f(x)$ has a removable discontinuity at $ x=0$. The discontinuity can be removed by setting $ f(0)=0.$ The discontinuity at $ x=1$ is non-removable -- it is a jump discontinuity.
