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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 39

  • question_answer
    If \[f(x)=\left\{ \begin{matrix}    2+x, & x\ge 0  \\    2-x, & x<0  \\ \end{matrix} \right.,\]then \[\underset{x\to 0}{\mathop{\lim }}\,\,f(f(x))\] is equal to

    A) \[2\]                 

    B)        \[4\]

    C) \[1\]                 

    D)        Does not exist

    Correct Answer: B

    Solution :

    [b] \[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,f\left( f(x) \right)=f\left( f({{0}^{+}}) \right)=f({{2}^{+}})=4\] \[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,f\left( f(x) \right)=f\left( f({{0}^{-}}) \right)=f({{2}^{+}})=4\]


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