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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • 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:

    A)  8                            

    B)         4

    C)  \[-8\]                   

    D)         11

    E)  44

    Correct Answer: B

    Solution :

    Given that \[3f(x)+2f\left( \frac{x+59}{x-1} \right)=10x+30\]                                ...(i) and\[3f\left( \frac{x+59}{x-1} \right)+2f(x)=\frac{40x+560}{x-1}\]     ...(ii) On solving Eqs. (i) and (ii), we get \[f(x)=\frac{6{{x}^{2}}-4x-242}{x-1}\] \[\therefore \]\[f(7)=\frac{6\times 49-28-242}{6}=\frac{294-270}{6}\]                                 \[=\frac{24}{6}=4\]


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