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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 11

  • question_answer
    Number of integral values in the range of the function \[f(x)={{\cot }^{-1}}x+\frac{1}{2}{{\cos }^{-1}}x\] is

    A) \[2\]                       

    B) \[3\]          

    C) \[4\]                       

    D) \[5\]

    Correct Answer: B

    Solution :

    [b] \[f(x)={{\cot }^{-1}}x+\frac{1}{2}{{\cos }^{-1}}x\] Domain:   \[[-1,\,1]\] \[f(x)\] is a decreasing function in \[[-1,\,1],\] Hence, range is \[[f(1),\,f(-1)]\]or \[\left[ \frac{\pi }{4},\frac{5\pi }{4} \right].\]       


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