JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Morning)

  • question_answer Le \[f(x)={{x}^{2}},x\in R.\]For any \[A\subseteq R,\]define\[g(A)=\{x\in R,f(x)\in A\}\]If \[S=\left[ 0,4 \right],\] then which one of the following statements is not true? [JEE Main 10-4-2019 Morning]

    A) \[f(g(S))\ne f(S)\]                     

    B) \[f(g(S))=S\]

    C) \[g(f(S))=g(S)\]           

    D) \[g(f(S))\ne (S)\]

    Correct Answer: C

    Solution :

    \[g\left( S \right)=\left[ 2,2 \right]\] So, \[f\left( g\left( S \right) \right)=\left[ 0,4 \right]=S\] And \[f(S)=[0,16]\Rightarrow f(g(S))\ne f(S)\] Also, \[g(f(S))=[-4,4]\ne g(S)\] So,\[g(f(S)\ne S\]         

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