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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2010

  • question_answer
    If\[f\]is a real valued function such that\[f(x+y)=f(x)+f(y)\]and\[f(1)=5,\]then the value of f(100) is

    A)  200                                       

    B)  300

    C)  350                       

    D)         400

    E)  500

    Correct Answer: E

    Solution :

    We have \[f(x+y)=f(x)+f(y)\]                ...(i) and            \[f(1)=5\]                               ...(ii) Now, \[f(100)=f(1+1+1+1+1\]\[+....+1,100times)\] Using Eq. (i), \[=f(1)+f(1)+f(1)+.....+f(1),100\text{ }times\] Using Eq. (ii) \[=5+5+5+5+...+5,100\text{ }times\] \[=5\times 100\] = 500


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