Find a function such $f(f(x))=-x$

Question

I was looking for an answer to this question for some days now:

Find a function f such that $f(f(x))=-x$

Please help, thank you!

Are there any restrictions? As it stands, the function $f(x)=ix$ will suffice, $i^2=-1$. — Daryl, Jan 08 '14 at 08:59

score 4 · Accepted Answer · answered Jan 08 '14 at 08:59

4

A function on what domain? On $\mathbb C$, $f(x) = ix$ will do.

On $\mathbb R$, there's no such function that is continuous. Hint: if $f: \mathbb R \to \mathbb R$ is continuous and one-to-one, it is either increasing or decreasing...

answered Jan 08 '14 at 08:59

Robert Israel

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Find a function such $f(f(x))=-x$

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