0
$\begingroup$

This question already has an answer here:

We are required to determine all continuous real valued functions $f$ such that $$f(f(x))=-x$$

I’ve determined that if such a function exists, it must be bijective. But I don’t know if such a function exists, let alone find all such functions. Any hints and suggestions will be appreciated.

$\endgroup$

marked as duplicate by Jyrki Lahtonen, José Carlos Santos real-analysis Oct 28 '18 at 16:42

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

1
$\begingroup$

Since it is injective, continuous and its domain is an interval, it must be monotonic. Then, $f\circ f$ is an increasing functions. Therefore, no such function exists.

$\endgroup$
  • $\begingroup$ Ah, nice. How did I miss that! Thanks for taking your time. $\endgroup$ – John Mitchell Oct 28 '18 at 16:38

Not the answer you're looking for? Browse other questions tagged or ask your own question.