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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    The function f satisfies the functional equation \[3f(x)+2f\left( \frac{x+59}{x-1} \right)=10x+30\] for all real \[x\ne 1\]. The value of \[f(7)\] is [Kerala (Engg.) 2005]

    A)            8

    B)            4

    C)            ?8

    D)            11

    E)            44

    Correct Answer: B

    Solution :

               \[3f(x)+2f\left( \frac{x+59}{x-1} \right)=10x+30\]            For \[x=7\], \[3f(7)+2f(11)=70+30=100\]                    For \[x=11\], \[3f(11)+2f(7)=140\]                    \[\frac{f(7)}{-20}=\frac{f(11)}{-220}=\frac{-1}{9-4}\] Þ \[f(7)=4\].


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