JEE Main & Advanced JEE Main Solved Paper-2014

  • question_answer
    If g is the inverse of a function f and \[(x)=\frac{1}{1+{{x}^{5}}},\]then g′ (x) is equal to :   JEE Main  Solved  Paper-2014

    A) \[1+{{x}^{5}}\]                 

    B) \[5{{x}^{4}}\]

    C) \[\frac{1}{1+{{\left\{ g(x) \right\}}^{5}}}\]                           

    D) \[1+{{\{g(x)\}}^{5}}\]

    Correct Answer: D

    Solution :

    \[g\{f(x)\}=x\] \[g'\{f(x)\}.f'(x)=1\Rightarrow g'\{f(x)\}=\frac{1}{f'(x)}\] \[\Rightarrow \]\[g'\{f(x)\}=1+{{x}^{5}}\] \[g'\left\{ f\left\{ g(x) \right\} \right\}=1+{{\left\{ g(x) \right\}}^{5}}\Rightarrow g'(x)=1+{{\left\{ g(x) \right\}}^{5}}\]

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