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JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    Suppose \[f:[2,\ 2]\to R\] is defined by  \[f(x)=\left\{ \begin{align}   & -1\,\,\,\,\,\,\,\,\,\,\,\,\,\text{for}\ -2\le x\le 0 \\  & x-1\ \ \ \ \ \text{for}\ 0\le x\le 2 \\ \end{align} \right.\], then \[\{x\in (-2,\ 2):x\le 0\] and \[f(|x|)=x\}=\] [EAMCET 2003]

    A) \[\{-1\}\]

    B) {0}

    C) \[\{-1/2\}\]

    D) \[\varphi \]

    Correct Answer: C

    Solution :

    By verification, \[f\left( \left| -\frac{1}{2} \right| \right)=f\left( \frac{1}{2} \right)=\frac{1}{2}-1=-\frac{1}{2}\]            Hence \[f(|x|)=x\].


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