Question 146
Let $\mathbb{R}$ be the set of real numbers. Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying the condition
$$
f(x f(y)-y)+f(x y-x)+f(x+y)=2 x y
$$
for all $x, y \in \mathbb{R}$.
$$
f(x f(y)-y)+f(x y-x)+f(x+y)=2 x y
$$
for all $x, y \in \mathbb{R}$.