$f(f(x))=x \ \forall x \in \mathbb{R}$. I am trying to prove there exists an irrational $t$ such that $f(t)$ is also irrational.
I have been trying things like assume $t$ irrational implies $f(t)$ is rational and then $f(f(t)+t)$ is rational but $f(f(f(t)+t))=f(t)+t$ but I can't come up with a contradiction. Is there a less mind-boggling approach?