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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        The domain of definition of\[f(x)={{\sin }^{-1}}(|x-1|-z)\]is

    A)  \[[-2,0]\cup [2,4]\]        

    B)  \[(-2,0)\cup (2,4)\]

    C)  \[[-2,0]\cup [1,3]\]        

    D)  \[[-2,0]\cup [1,3]\]

    Correct Answer: A

    Solution :

                                    \[f(x)\] is defined for \[-1\le |x-1|-2\le 1\] \[\Rightarrow \]               \[1\le |x-1|\le 3\] \[\Rightarrow \] \[1\le (x-1)\le 3\]or \[-3\le x-1\le -1\] \[\Rightarrow \] \[2\le x\le 4\]   or            \[-2\le x\le 0\] \[\Rightarrow \]               \[x\in [2,4]\cup [-2,0]\]


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