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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    The number of points at which the function \[f(x)=\frac{1}{{{\log }_{e}}\left| x \right|}\] is discontinuous, is

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: C

    Solution :

    [c] The function \[\log \left| x \right|\] is not defined at \[x=0\]. So, \[x=0\] is a point of discontinuity Also, for \[f(x)\] to be defined; \[\log \left| x \right|\ne 0\Rightarrow x\ne \pm 1\] Hence, \[0,1,-1\] are three points of discontinuity.


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