Question 113
Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that for any two real numbers $x$ and $y$,
$$
f(2xy)^2 + f(f(x)^2 - y^2)^2 = f(x^2 + y^2)^2.
$$
$$
f(2xy)^2 + f(f(x)^2 - y^2)^2 = f(x^2 + y^2)^2.
$$
MathNet 2019-part-03 — 184 problems (EN–VI) Question 113
Math Olympiad Vault · MathNet 2019-part-03 — 184 problems (EN–VI)