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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        If\[f:R\to S\] defined by \[f(x)=\sin x-\sqrt{3}\cos x+1,\]is onto, then the interval of S is

    A)  [0, 1]                                    

    B) \[[-1,1]\]

    C)  [0, 3]                                    

    D) \[[-1,3]\]

    Correct Answer: D

    Solution :

                    Since, \[-2\le \sin x-\sqrt{3}\cos x\le 2\] \[\Rightarrow \]               \[-1\le \sin x-\sqrt{3}\cos x+1\le 3\] Here, range of\[f(x)\]is\[[-1,\text{ }3]\]. For\[f\]to be onto, \[f=[-1,3]\]


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