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

  • question_answer
    If \[f(g\,f(x))=g(f(x))=x\]  for all real numbers \[x\]  and \[f(2)=5\] and \[f(5)=3,\]then the value of \[g(3)+g(f(2))\] is

    A)  7                                

    B)  5

    C)  3                                

    D)  2

    Correct Answer: A

    Solution :

    Since g and f are inverses \[g(3)=5\] and so \[g(3)+g(2(2))\,=5+2=7\] \[{{g}^{-1}}(x)\,=f(x)\] and \[{{f}^{-1}}(x)=g(x)\] \[f(2)=5\] \[{{f}^{-1}}(5)\,=2;\,\,\,g(5)=2\] \[{{f}^{-1}}(3)=5;\,\,g(3)=5\]


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