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

  • question_answer
    The number of linear functions f satisfying \[f(x+f(x))=x+f(x)\forall x\in R\] is

    A) 0

    B) 1

    C) 2

    D) 3

    Correct Answer: C

    Solution :

    [c] Let \[f(x)=ax+b\]                   (1) \[\Rightarrow f(ax+b+x)=x+ax+b\] \[\Rightarrow f((a+1)x+b)=(a+1)x+b\] Replace \[(a+1)x+b\]by, y, we have \[\Rightarrow f(y)=(a+1)\left( \frac{y-b}{a+1} \right)+b\] Or \[f(x)=(a+1)\left( \frac{x-b}{x+1} \right)+b\] \[\therefore \] Required no, of linear functions is 2.


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