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KVPY Sample Paper KVPY Stream-SX Model Paper-10

  • question_answer
    If \[f\,(x)={{x}^{x}};\]\[[a,\,\,\infty )\to [b,\,\,\infty )\] is an invertible function then the minimum value of a & b are

    A) \[\frac{1}{e},\]\[{{e}^{-1/e}}\]             

    B) e, \[{{e}^{1/e}}\]

    C) \[\frac{1}{e},\]                          

    D) none of these

    Correct Answer: A

    Solution :

    \[f\,(x)={{x}^{x}}\]
    \[f'(x)={{x}^{x}}(1+\ln x)=0\]  \[\Rightarrow \]   \[x=\frac{1}{e}\]
    \[\therefore \]      \[a=\frac{1}{e}\] & \[b={{e}^{-\,\frac{1}{e}}}\]


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