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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 7

  • question_answer
    If {} denotes the fractional part of x, the range of the function \[f(x)=\sqrt{{{\{x\}}^{2}}-2\{x\}}\]is

    A) \[\phi \]                        

    B) \[[0,1/2]\]

    C) \[\{0,1/2\}\]                            

    D) \[\{0\}\]

    Correct Answer: D

    Solution :

    \[\{{{x}^{2}}\}-2\{x\}\ge 0\] \[\Rightarrow \,\,\{x\}\,(\{x\}-2\}\ge 0\] \[\Rightarrow \,\,\{x\}\,\le 0\] or \[\,\{x\}\,\ge 2\] Second case is not possible. Hence \[\,\{x\}\,=0\]as \[\,\{x\}\,\le [0,1)\] Hence range of \[f(x)\] contains only one element 0.


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