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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    If\[f:R\to R\]is defined by\[f(x)=3x+|x|,\]then \[f(2x)-f(-x)-6x\]is equal to:

    A)  \[3f(x)\]                             

    B)  \[2f(x)\]             

    C)         \[-f(x)\]              

    D)         \[f(-x)\]

    E)  \[f(x)\]

    Correct Answer: E

    Solution :

    We have, \[f(x)=3x+|x|\] \[f(2x)=6x+|2x|\] \[f(-x)\,=-3x+|-x|\,=-3x+|x|\] \[\therefore \]\[f(2x)-f(-x)-6x=6x+|2x|+3x-|x|-6x\]      \[=3x+|x|=f(x)\]


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