JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\] is            [AIEEE 2004]           

    A)            [1, 2)

    B)            [2, 3)

    C)            [1, 2]

    D)            [2, 3]

    Correct Answer: B

    Solution :

               To define \[f(x)\], \[9-{{x}^{2}}>3\Rightarrow -3<x<3\]      .....(i)                    \[-1\le (x-3)\le 1\Rightarrow 2\le x\le 4\]                           .....(ii)                    From (i) and (ii), \[2\le x<3\] i.e., [2, 3).


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