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JEE Main & Advanced Sample Paper JEE Main Sample Paper-22

  • question_answer
    Range of the function\[f(x)=4{{\tan }^{-1}}x+3{{\sin }^{-1}}x+{{\sec }^{-1}}x\text{ }\]is

    A) \[\left\{ \frac{-3\pi }{2},\frac{-5\pi }{2} \right\}\]

    B)  \[\left\{ \frac{3\pi }{2},\frac{5\pi }{2} \right\}\]

    C) \[\left( \frac{-3\pi }{2},\frac{5\pi }{2} \right)\]

    D) \[\left\{ \frac{-3\pi }{2},\frac{5\pi }{2} \right\}\]

    Correct Answer: D

    Solution :

    Domain of f(x) is \[x\in R\,\cap x\in [-1,\,\,1]\,\cap \,|x|\ge 1\] \[\Rightarrow \,\,\,\,\,\,\,\,x\in \,\{-1,\,\,1\}\] \[\Rightarrow \]   Range of f(x) contains \[\{f(-1),\,\,f(1)\}\] i.e.          \[\left\{ \frac{-3\pi }{2},\,\frac{5\pi }{2} \right\}\]


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