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BCECE Engineering BCECE Engineering Solved Paper-2013

  • question_answer
    If f and g be differentiable function satisfying \[g(a)=2,g(a)=b\]and\[fog=I\] (identity function), then \[f(b)\]is equal to

    A)  \[\frac{1}{2}\]                  

    B)         2                            

    C)  \[\frac{2}{3}\]                  

    D)         None of these

    Correct Answer: A

    Solution :

    Since, \[fog=l\] \[\Rightarrow \]\[fog(x)=x,\]for all \[x\] \[\Rightarrow \]\[f\{g(x)\}.g(x)=1\]for all\[x.\] \[\Rightarrow \]\[f\{g(a)\}=\frac{1}{g(a)}=\frac{1}{2}\] \[f(b)=\frac{1}{2}\]                                                                         \[[\because \,g(a)=b]\]


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