Question 147
Let $\mathbb{R}$ be the set of all real numbers. Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that for any $x, y \in \mathbb{R}$, there holds
$$
f(x + f(y)) + f(xy) = y f(x) + f(y) + f(f(x)).
$$
$$
f(x + f(y)) + f(xy) = y f(x) + f(y) + f(f(x)).
$$