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JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relations and Functions-I

  • question_answer
    If \[f(x)={{e}^{-x}},\] then \[\frac{f(-a)}{f(b)}\] is equal to

    A) \[f(a+b)\]

    B)        \[f(a-b)\]

    C) \[f(-a+b)\]

    D)        \[f(-a-b)\]

    Correct Answer: D

    Solution :

    [d] \[\frac{f(-a)}{f(b)}=\frac{{{e}^{a}}}{{{e}^{-b}}}={{e}^{a}}{{e}^{b}}={{e}^{a+b}}={{e}^{-(-a-b)}}\] \[=f(-a-b)\]


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