Question 121
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$, such that for all real $x, y$ the following equality holds:
$$
f(x + x y + f(y)) = (f(x) + \frac{1}{2})(f(y) + \frac{1}{2}).
$$
$$
f(x + x y + f(y)) = (f(x) + \frac{1}{2})(f(y) + \frac{1}{2}).
$$