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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\]is

    A)  [1,2]                                     

    B)  [2,3]

    C)  [2,3)                                     

    D)  [1,2)

    Correct Answer: C

    Solution :

                    For\[f(x)\]to be defined, \[9-{{x}^{2}}>0\] \[\Rightarrow \]           \[{{x}^{2}}<9\]       \[\Rightarrow \]               \[-3<x<3\]                         ...(i) And        \[-1\le x-3\le 1\]                               \[\Rightarrow \]               \[2\le x\le 4\]                ...(ii) From Eqs. (i) and (ii), we get \[2\le x<3\]


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