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JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    The function \[f(x)=\max [(1-x),\,(1+x),\,2],\] \[x\in (-\infty ,\,\infty ),\]is [IIT 1995]

    A) Continuous at all points

    B) Differentiable at all points

    C) Differentiable at all points except at \[x=1\]and \[x=-1\]          

    D) Continuous at all points except at \[x=1\]and \[x=-1\]where it is discontinuous

    Correct Answer: C

    Solution :

    •  \[f(x)=\max \,\,\left\{ (1-x),\,\,(1+x),\,\,2 \right\},\,\,\forall \,\,x\in (-\,\infty ,\,\infty ).\] \[f(x)=\left\{ \begin{array}{*{35}{r}}    1+x; & x>1  \\    2; & -1\le x\le 1  \\    1-x; & x           
    • \ \[f(x)\] is differentiable at all the points, except at           
    • \[x=1\] and at \[x=-1\]                                             .....(ii)


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