If `f(x)` defined by `f(x)={(|x^2-x|)/(x^2-|x|),x!=0,1-1`. Then (A)f(x) is continuous for all `x` (B) for all `x` except `x=0` (C) for all `x` except `x=1` (D) for all `x` except `x=0` and `x=1`

Explanation

Given, $$f(x)=\left\{\begin{array}{l}\frac{x^{2}-x}{x^{2}-x}=1, \text { if } \quad x<0 \quad \text { or } \quad x>1 \\ -\frac{\left(x^{2}-x\right)}{\left(x^{2}-x\right)}=-1, \text { if } \quad 01 \\ -1, \text { if } \quad 0