Functional equation

[myra_panama]

Let $ A = \{a+b \sqrt{2} \mid a,b\in \mathbb{Z}\}$ and $f\colon A\to A$ such that $2f(f(x)) + f(x)=x$. Find f.

Исправил..

[Carden]

Are f and A connected?
Casually guessed that $f(x)=\frac{x}2$