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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

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

    A)  [2, 3]                                    

    B)  [2, 3)

    C)  [1, 2]                                    

    D)  [1, 2)

    Correct Answer: B

    Solution :

                    The function\[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\]will be defined, if      (I)  \[-1\le x(x-3)\le 1\Rightarrow 2\le x\le 4\]                         ...(i) (II) \[9-{{x}^{2}}>0\Rightarrow -3<x<3\]                                   ...(ii) From relations (i) and (ii), we get                 \[2\le x<3\] \[\therefore \]Domain of the given function = [2, 3).


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