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JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relations and Functions-I

  • question_answer
    The domain of the real valued function \[f(x)=\sqrt{5-4x-{{x}^{2}}}+{{x}^{2}}\log (x+4)\] is

    A) \[(-5,1)\]

    B)        \[-5\le x\,\,and\,\,x\ge 1\]

    C) \[\left( -4,1 \right]\]

    D)        \[\phi \]

    Correct Answer: C

    Solution :

    [c] \[f(x)=\sqrt{5-4x-{{x}^{2}}}+{{x}^{2}}\log (x+4)\] \[\Rightarrow 5-4x-{{x}^{2}}\ge 0,x+4>0\] \[\Rightarrow (x+5)(x-1)\le 0,x>-4\] \[\Rightarrow -5\le x\le 1,x>-4\Rightarrow -4<x\le 1.\]


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