Question 64
Find all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying the equation
$$
f(x+y) + f(x)f(y) = (1+y)f(x) + (1+x)f(y) + f(xy), \quad (1)
$$
for all $x, y \in \mathbb{R}$.
$$
f(x+y) + f(x)f(y) = (1+y)f(x) + (1+x)f(y) + f(xy), \quad (1)
$$
for all $x, y \in \mathbb{R}$.