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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 33

  • question_answer
    The domain of the function \[\operatorname{f}(x) = log \left( \sqrt{x-4} + \sqrt{6-x} \right)\] is

    A) \[[4,\,\,\infty )\]  

    B)        \[(\infty ,\,\,6]\]

    C) [4, 6]    

    D)        None of these

    Correct Answer: C

    Solution :

    \[\operatorname{f}(x)=log\,\left( \sqrt{x\,-4}+\sqrt{6-x} \right)\] \[\Rightarrow \,\,x-4\ge 0\,\,and\,\,6-x\ge 0\,\,\Rightarrow \,\,x\ge 4\,\,and\,\,x\le 6\] \[\therefore  \,\,Domain of\,\,f(x) = \left[ 4,\,\,6 \right].\]


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