• # question_answer Let $f\left( x \right)=\left[ x \right]+\left| 1-x \right|,-1\le x<3,$ (here [.] denotes greatest integer function). The number of points, where $f\left( x \right)$ is non-differentiable is A) 5 B) 0 C) 2 D) none of these

 $y=\left[ x \right]+\left| 1-x \right|\operatorname{for}-1\le x<3$ (i) For $-1\le x<1,y=-1+1-x=-x$ (ii) For $0\le x<1,\,\,\,\,\,\,y=0+1-x=1-x$ (iii) For $1\le x<2\,\,\,\,\,\,y=1+x-1=x$ (iv) For $2\le x<3,\,\,\,\,\,\,y=2+x-1=x+1.$
 Given function is discontinuous at $x=0,1,2,$ Given function is not differentiable at $x=0,1,2.$