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 function can be simplified as,

`f(x)={1, if x≤0 or x>1`


`−1,if 0
Now,
`lim​_(x→0−)1=1` and `lim​_(x→0+)f(x)=lim​_(x→0)−1=−1`

Clearly, `lim_(x→0−)​f(x)!=lim​_(x→0+)f(x)`

So, f(x) is not continuous
at `x=0` It can be easily seen
that it is not continuous at `x=1` also.