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

  • question_answer
    If \[3f(x)-f\left( \frac{1}{x} \right)=\log {{x}^{4}},\] then \[f({{e}^{-x}})\] is

    A) \[1+x\]

    B)        \[1/x\]

    C) \[x\]

    D)        \[-x\]

    Correct Answer: D

    Solution :

    [d] \[3f(x)-f\left( \frac{1}{x} \right)=\log {{x}^{4}};\,\,\,\,x\equiv \frac{1}{x}\] \[3+\left( \frac{1}{x} \right)-f(x)=log{{\left( \frac{1}{x} \right)}^{4}}\] After solving we get \[f(x)=log\,\,x\] \[f({{e}^{-x}})=lo{{g}_{e}}{{e}^{-x}}=-x\]


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