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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    If \[f(x)=\frac{1}{\sqrt{-x}},\] then domain of fof is

    A)  \[(0,\,\,\infty )\]

    B)  \[(-\,\infty ,\,\,0)\]

    C)  \[\{0\}\]

    D)  \[\{\,\,\}\]

    Correct Answer: D

    Solution :

    Given that,  \[f(x)=\frac{1}{\sqrt{-x}}\] \[\therefore \] \[fof\,(x)=f(f(x))=f\left( \frac{1}{\sqrt{-x}} \right)\] \[\Rightarrow \] \[fof(x)=\frac{1}{\sqrt{-\frac{1}{\sqrt{-x}}}}\] Since \[\sqrt{-\frac{1}{\sqrt{-x}}}\] is an imaginary. Hence, no domain of fof (x) exist.


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