Question 7
Show that there is no function $f: \mathbb{R}_{\gt 0} \rightarrow \mathbb{R}_{\gt 0}$ such that for all $x, y \in \mathbb{R}_{\gt 0}$:
$$
f(x f(x)+y f(y))=x y
$$
$$
f(x f(x)+y f(y))=x y
$$
MathNet 2018-part-06 — 181 problems (EN–VI) Question 7
Math Olympiad Vault · MathNet 2018-part-06 — 181 problems (EN–VI)