Question 36
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that
$$
f(f(x) f(1-x))=f(x) \quad \text{ and } \quad f(f(x))=1-f(x)
$$
for all real $x$.
$$
f(f(x) f(1-x))=f(x) \quad \text{ and } \quad f(f(x))=1-f(x)
$$
for all real $x$.
MathNet 2022-part-04 — 197 problems (EN–VI) Question 36
Math Olympiad Vault · MathNet 2022-part-04 — 197 problems (EN–VI)