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

  • question_answer
    Let f and g be functions from R To R defined as \[f(x)=\left\{ \begin{matrix}    7{{x}^{2}}+x-8,x\le 1  \\    4x+5,1<x\le 7  \\    8x+3,x>7  \\ \end{matrix},g(x)=\left\{ \begin{matrix}    \left| x \right|,x<-3  \\    0,-3\le x<2  \\    {{x}^{2}}+4,x\ge 2  \\ \end{matrix} \right. \right.\] Then

    A) \[(fog)(-3)=8\]

    B) \[(fog)(9)=683\]

    C) \[(gof)(0)=-8\]

    D) \[(gof)(6)=427\]

    Correct Answer: B

    Solution :

    [b] we have \[g(-3)=0\] \[\Rightarrow f(g(-3))=f(0)=7{{(0)}^{2}}+0-8=-8\] \[\therefore fog(-3)=-8\] \[g(9)={{9}^{2}}+4=85\] \[\Rightarrow f(g(9))=f(85)=8.85+3=683\] \[\therefore fog(9)=683\] \[f(0)={{7.0}^{2}}+0-8=-8\] \[\Rightarrow g(f(0))=g(-8)=\left| -8 \right|=8\] \[f(6)=4.6+5=29\] \[\Rightarrow g(f(6))=g(29)={{(29)}^{2}}+4=845\] \[\therefore gof(6)=845\]


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