Question 132
Find all real numbers $a$ such that there exists a function $f: \mathbb{R} \to \mathbb{R}$ satisfying the following conditions:
1) $f(f(x)) = x f(x) - a x$ for all real $x$;
2) $f$ is not constant;
3) $f$ takes the value $a$.
1) $f(f(x)) = x f(x) - a x$ for all real $x$;
2) $f$ is not constant;
3) $f$ takes the value $a$.