Question 14
Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying the condition
$$
f\left(y^{2}+2 x f(y)+f(x)^{2}\right)=(y+f(x))(x+f(y))
$$
for all real numbers $x$ and $y$.
$$
f\left(y^{2}+2 x f(y)+f(x)^{2}\right)=(y+f(x))(x+f(y))
$$
for all real numbers $x$ and $y$.