Answer
$ f(x)=\frac{x-2}{|x-1|}$ is discontinuous at $ x=1$ and the discontinuity is infinite. The function is niether left- nor right- continuous at $ x=1$.
Work Step by Step
Since $\lim\limits_{x \to 1}\frac{x-2}{|x-1|}=\infty $, then the function $ f(x)=\frac{x-2}{|x-1|}$ is discontinuous at $ x=1$ and the discontinuity is infinite. The function is niether left- nor right- continuous at $ x=1$.
