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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

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

    A)  \[1\]

    B)  \[2\]

    C)  \[3\]

    D)  \[\infty \]

    Correct Answer: C

    Solution :

    Given,  \[f(x)=\frac{1}{{{\log }_{e}}\,|x|}\] On differentiating w. r. t. x, we get \[f'(x)=-\frac{1}{{{({{\log }_{e}}\,|x|)}^{2}}}\,\left( \frac{1}{x} \right)\] Here, \[f'(x)\] does not exist at \[x=0,\,-1\,\]and 1. Hence, \[f(x)\] is discontinuous at three points of x.


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