JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

  • 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, 3]                                    

    B)  \[[-1,\text{ }1]\]

    C)  [0, 1]                                    

    D)  \[[-1,\text{ }3]\]

    Correct Answer: D

    Solution :

                    Since\[-2\le \sin x-\sqrt{3}\cos x\le 2\] \[\Rightarrow \]\[-1\le \sin x-\sqrt{3}\cos x+1\le 3\] \[\therefore \]Range of\[f(x)=[-1,3]\].


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