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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 26

  • question_answer
    The number of points on the real line where the function  \[f(x)={{\log }_{|{{x}^{2}}-1|}}|x-3|\]is not denned is

    A) \[4\]                       

    B)        \[5\]                       

    C) \[6\]                 

    D)        \[7\]

    Correct Answer: C

    Solution :

         [c] \[{{\log }_{|{{x}^{2}}-1|}}|x-3|\] is defined when \[x-3\ne 0\] and \[|{{x}^{2}}-1|>0\] and \[|{{x}^{2}}-1|\,\,\ne \,\,1.\] \[\Rightarrow \,\,\,x\ne 3,\,\,{{x}^{2}}-1\ne 0\] i.e., \[x\ne 1\] or \[-1\] \[|{{x}^{2}}-1|\,\,\ne 1\Rightarrow x\ne -\sqrt{2}\] or \[\sqrt{2};\]  \[x\ne 0\]          Therefore, the points at which the function is not defined are \[x=0,\,1,-1,\sqrt{2},-\sqrt{2},3.\]


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