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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    The domain of the function \[f(x)={{\sin }^{-1}}\{{{(1+{{e}^{x}})}^{-1}}\}\] is                                                               [AMU 1999]           

    A)            \[\left( \frac{1}{4},\ \frac{1}{3} \right)\]

    B)             [?1, 0]

    C)            [0, 1]

    D)            [?1, 1]

    Correct Answer: A

    Solution :

               Clearly \[-1\le \frac{1}{1+{{e}^{x}}}\le 1\]            But \[2<{{e}^{x}}<3\] Þ \[3<({{e}^{x}}+1)<4\]Þ \[\frac{1}{4}<\frac{1}{1+{{e}^{x}}}<\frac{1}{3}\]            \Domain of \[f(x)=\left( \frac{1}{4},\,\frac{1}{3} \right)\].


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