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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 25

  • question_answer
    Let \[F(x)=lo{{g}_{e}}x+{{\log }_{x}}e,\] then the domain of the function \[\frac{1}{\sqrt{|f(x)|-f(x)}}\] is

    A) \[(0,1)\] 

    B)        \[(1,\infty )\]

    C) \[(1,e)\]             

    D) \[(-\infty ,\infty )\]

    Correct Answer: A

    Solution :

    [a] : The function\[\frac{1}{\sqrt{|f(x)|-f(x)}}\]will be defined, when\[|f(x)|>f(x)\] \[\Rightarrow \]\[f(x)<0\Rightarrow lo{{g}_{e}}x+{{\log }_{x}}e<0\] \[\Rightarrow \]\[\frac{{{(lo{{g}_{e}}x)}^{2}}+1}{{{\log }_{e}}x}<0\] \[\Rightarrow \]\[{{\log }_{e}}x<0\Rightarrow x<{{e}^{0}}\Rightarrow x<1\Rightarrow 0<x<1\]


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