KVPY Sample Paper KVPY Stream-SX Model Paper-25

  • 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

    Correct Answer: D

    Solution :

    \[y=\left[ x \right]+\left| 1-x \right|\operatorname{for}-1\le x<3\]
    (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
    Given function is not differentiable at

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