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JEE Main & Advanced JEE Main Paper Phase-I (Held on 09-1-2020 Evening)

  • question_answer
    Let f and g be differentiable functions on R such that fog is the identity function. If for some a, \[b\in R,\] \[g'(a)=5\] and \[g(a)=b,\] then \[f'(b)\] is equal to: [JEE MAIN Held on 09-01-2020 Evening]

    A) \[1\]

    B) \[5\]

    C) \[\frac{1}{5}\]

    D) \[\frac{2}{5}\]

    Correct Answer: C

    Solution :

    \[\because \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,f(g(x)=x\] Differentiating w.r.t. x \[f'(g(x).g'(x)=1\] Put    \[x=a\] \[f'(g(a)\cdot g'(a)=1\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,f'(b)\cdot 5=1\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,f'(b)=\frac{1}{5}\]


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