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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    Let \[f:R\to R\] be defined by \[f(x)=2x+|x|\], then \[f(2x)+f(-x)-f(x)=\] [EAMCET 2000]

    A)            \[2x\]

    B)            \[2|x|\]

    C)            \[-2x\]

    D)            \[-2|x|\]

    Correct Answer: B

    Solution :

               \[f(2x)=2(2x)+|2x|\,=4x+2|x|\],            \[y={{x}^{2}}+1\],            \[f(x)=2x+|x|\] Þ \[f(2x)+f(-x)-f(x)\]                    \[=4x+2|x|+|x|-2x-2x-|x|\]\[=2\,\,|x|\].


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