Question 15
Find all surjective functions $f: (0, +\infty) \to (0, +\infty)$ such that
$$
2x \cdot f(f(x)) = (f(f(x)) + x) \cdot f(x)
$$
for all $x \in (0, +\infty)$.
A function $f: A \to B$ is said to be surjective iff the range of $f$ is $B$, that is, for all $y \in B$ there exists $x \in A$ such that $f(x) = y$.
$$
2x \cdot f(f(x)) = (f(f(x)) + x) \cdot f(x)
$$
for all $x \in (0, +\infty)$.
A function $f: A \to B$ is said to be surjective iff the range of $f$ is $B$, that is, for all $y \in B$ there exists $x \in A$ such that $f(x) = y$.