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I was wondering if there is a continuous function such that $f(f(x)) = xf(x)$ for every positive number $x$.

  • 0
    $f(x) = 0$ for $\forall x$ :)2012-09-29
  • 1
    You must have $f(1)=0$ or $1$.2012-09-29
  • 1
    Did you mean to require $f(x)$ to be positive as well?2012-09-30
  • 0
    At the invertible places, the equation also reads $f(x)=x\cdot f^{-1}(x)\ $.2012-09-30

3 Answers 3