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JCECE Engineering JCECE Engineering Solved Paper-2003

  • question_answer
    The domain of the function\[y=\frac{1}{\sqrt{|x|-x}}\]is:

    A) \[(-\infty ,\,\,0)\]                            

    B) \[(+\infty ,\,\,0)\]

    C) \[(-\infty ,\,\,-1)\]                          

    D)  \[(-\infty ,\,\,\infty )\]

    Correct Answer: A

    Solution :

    Given,   \[y=\frac{1}{\sqrt{|x|-x}}\] When    \[x\ge 0\]                 \[y=\frac{1}{\sqrt{x-x}}=\infty \]                              (not defined) When    \[x<0\]                 \[y=\frac{1}{\sqrt{-x-x}}=\frac{1}{\sqrt{-2x}}\] \[\therefore \]Given function is defined for every negative values of\[x\]. \[\therefore \]Required domain is\[(-\infty ,\,\,0)\].


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