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JEE Main & Advanced Mathematics Equations and Inequalities Question Bank Self Evaluation Test - Linear Inequalities

  • question_answer
    The set of real value of x satisfying \[\left| |x-1|-1 \right|\le 1\]is

    A) \[[-1,3]\]

    B) \[[0,2]\]

    C) \[[-1,1]\]

    D) None of these  

    Correct Answer: A

    Solution :

    [a] \[\left| \left| x-1 \right|-1 \right|\le 1\Rightarrow -1\le \left| x-1 \right|-1\le 1\] \[\Rightarrow 0\le \left| x-1 \right|\le 2\Rightarrow -2\le x-1\le 2\] \[\Rightarrow -1\le x\le 3\Rightarrow x\in [-1,3]\]


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