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

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

    A) \[f(x)\]

    B)        \[2f(x)\]

    C) \[-f(x)\]

    D)        \[f(-x)\]

    Correct Answer: A

    Solution :

    [a] \[f(x)=3x+\left| x \right|\] \[\therefore f(2x)-f(-x)-6x=\] \[6x+\left| 2x \right|-3(-x)-\left| -x \right|-6x\] \[=3x+2\left| x \right|-\left| x \right|=3x+\left| x \right|=f(x)\]


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