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JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relation and Functions-II

  • question_answer
    Let \[f(x)=-1+\left| x-1 \right|,-1\le x\le 3\] and \[\le g(x)=2-\left| x+1 \right|,-2\le x\le 2,\] then \[(fog)(x)\], is equal to

    A) \[\left\{ \begin{matrix}    x+1-2\le x\le 0  \\    x-10<x\le 2  \\ \end{matrix} \right.\]

    B) \[\left\{ \begin{matrix}    x-1-2\le x\le 0  \\    x+10<x\le 2  \\ \end{matrix} \right.\]

    C) \[\left\{ \begin{matrix}    -1-x-2\le x\le 0  \\    x-10<x\le 2  \\ \end{matrix} \right.\]

    D) None of these

    Correct Answer: D

    Solution :

    [d] \[(fog)(x)=\left\{ \begin{matrix}    f(x+3),1\le x+3\le 2  \\    f(-x+1),-1\le x+2\le 2  \\ \end{matrix} \right.\] \[=\left\{ \begin{matrix}    \begin{align}   & f(x+3),1\le x+3\le 2 \\  & f(-x+1),\,-1\le -x+1\le 1 \\ \end{align}  \\    f(-x+1),\,1\le -x+1\le 2  \\ \end{matrix} \right.\] \[=\left\{ \begin{matrix}    \begin{align}   & x+1,-2\le x\le -1 \\  & -x-1,\,-1\le x\le 0 \\ \end{align}  \\    x-1,\,0\le x\le 2  \\ \end{matrix} \right.\]


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