Question 166
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ for which there exists a real $A$ satisfying $A \gt f(x)$ for every $x \in \mathbb{R}$, and such that for all reals $x, y$ we have:
$$
f(x f(y)) + y f(x) = x f(y) + f(x y)
$$
$$
f(x f(y)) + y f(x) = x f(y) + f(x y)
$$