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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    The domain of the function \[f(x)=\sqrt{x-{{x}^{2}}}+\sqrt{4+x}+\sqrt{4-x}\] is [AMU 1999]

    A)                    \[[-4,\ \infty )\]

    B)             [?4, 4]

    C)            [0, 4]

    D)            [0, 1]

    Correct Answer: D

    Solution :

               \[f(x)=\sqrt{x-{{x}^{2}}}+\sqrt{4+x}+\sqrt{4-x}\]            Clearly \[f(x)\] is defined, if \[4+x\ge 0\] Þ \[x\ge -4\]            \[4-x\ge 0\] Þ \[x\le 4\]            \[x(1-x)\ge 0\] Þ \[x\ge 0\] and \[x\le 1\]                    \ Domain of \[f=(-\infty ,\,4]\cap [-4,\,\infty )\cap [0,\,1]\]\[=[0,\,1]\].


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