f(x) is not defined at x = 1. For x ≥ 1 , f (x) = $\frac{\left|x-1\right|}{x-1}$ = $\frac{x-1}{x-1}$ = 1 For x < 1, f (x) = $\frac{\left|x-1\right|}{x-1}$ = $\frac{-(x-1)}{x-1}$ = $\frac{1-x}{x-1}$ = - 1 Thus, range of the function is either -1 or 1 at all the points and is undefined at x = 1