What can be $f$ so that $f^2(x) = -x$ for all $x\in R$?
I know that if $f^2(x) = -x$ then $f(x)$ is injective and $f$ can not be continuous.
But I can not find an example of discontinuous function so that $f^2(x) = -x$ for all $x\in R$.
Can anyone help me?