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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    If \[f(x)={{\log }_{a}}x\] and \[F(x)={{a}^{x}}\], then \[F[f(x)]\] is            [SCRA 1996]

    A)                    \[f[F(x)]\]

    B)            \[f[F(2x)]\]

    C)                    \[F|f(2x)|\]

    D)            \[F[(x)]\]

    Correct Answer: A

    Solution :

     \[F\,[f(x)]=F\,({{\log }_{a}}x)={{a}^{{{\log }_{a}}x}}=x\]                    \[f\,[F\,(x)]=f({{a}^{x}})={{\log }_{a}}{{a}^{x}}=x\,{{\log }_{a}}a=x\].


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