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JEE Main & Advanced Mathematics Functions Question Bank Differentiability

  • question_answer
    Let                                                                                  \[f(x)=\left\{ \begin{matrix}    \,\,\,\,\,\,\,\,\sin x, & \text{for }x\ge 0  \\    1-\cos x, & \text{for }x\le 0  \\ \end{matrix} \right.\]  and                                                                                           \[g(x)={{e}^{x}}\] . Then                                                                                               \[(gof)'(0)\]  is [UPSEAT 2004]

    A)            1

    B)            ?1

    C)            0

    D)            None of these

    Correct Answer: C

    Solution :

                                                                                                      \[(gof)\,(x)=g[f(x)]\]  =                                                                 \[g\,[1-\cos x]={{e}^{1-\cos x}},\text{ for }x\le 0\]                                                                                                                        \[(gof{)}'(x)={{e}^{1-\cos x}}.\sin x,\,\text{for  }x\le 0\]                                                                                                                                                                                      \[(gof{)}'(0)=0\].


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