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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 28

  • question_answer
    Let f and g be two real valued functions such that \[f(2-x)=2-f(x)\]and \[f(x)-g(x)=1\forall x\in R,\]then                     

    A) \[f(x)\] is symmetrical about the line \[x=1\]               

    B) \[g(x)\] is symmetrical about the line \[x=1\]

    C) \[f(x)\] is symmetrical about the point \[(1,0)\]

    D) \[g(x)\]is symmetrical about the point \[(1,0)\]

    Correct Answer: D

    Solution :

    [d] Given that \[f(x)-g(x)=1\] \[\Rightarrow \,\,\,\,f(x)-1=g(x)\] Also, \[f(2-x)=2-f(x)\] \[\Rightarrow \,\,\,f(2-x)-1=-(f(x)-1)\] \[\Rightarrow \,\,\,\,\,\,\,g(2-x)=-g(x)\] \[\Rightarrow \,\,\,\,\,\,\,g(x)=-g(2-x)\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,g(1+x)=-g(1-x)\] Thus, g is symmetrical about the point\[(1,0)\].


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