Mathematics

Problem

Define the function

f(x)= \begin{cases} \dfrac{x^{2}-1}{x-1}, & x<1,\\ 4, & x=1,\\ 3-x, & 1<x<2,\\ \ln(x-2), & x\ge 2. \end{cases}

List every point at which

f

is discontinuous and, for each point, state whether the discontinuity is removable, jump, or infinite.