Question 110
Do there exist numbers $a, b \in \mathbb{R}$ and a surjective function $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(f(x)) = b x f(x) + a
$$
for all real $x$?
$$
f(f(x)) = b x f(x) + a
$$
for all real $x$?
MathNet 2015-part-01 — 191 problems (EN–VI) Question 110
Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)