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JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    If \[f:R\to R\] and \[g:R\to R\] are given by \[f(x)=\ |x|\] and \[g(x)=\ |x|\] for each \[x\in R\], then \[\{x\in R\ :g(f(x))\le f(g(x))\}=\]  [EAMCET 2003]

    A) \[Z\cup (-\infty ,\ 0)\]

    B) \[(-\infty ,0)\]

    C) Z

    D) R

    Correct Answer: D

    Solution :

    • \[g(f(x))\le f(g(x))\] Þ \[g(|x|)\le f[x]\] Þ \[[|x|]\,=\,|[x]|\].                   
    • This is true for \[x\in R.\].


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