Question 5
Solve the functional equation $$
f(x+f(x+y)) + f(xy) = x + f(x+y) + yf(x)
$$ for $f \colon \mathbb{R} \to \mathbb{R}$. The equation must hold for all real numbers $x,y$.
f(x+f(x+y)) + f(xy) = x + f(x+y) + yf(x)
$$ for $f \colon \mathbb{R} \to \mathbb{R}$. The equation must hold for all real numbers $x,y$.