Question 57
Find all functions $f:\mathbb R\to\mathbb R$ satisfying
$$f(x+xy+f(y))=\left(f(x)+\frac12\right)\left(f(y)+\frac12\right)$$
for all $x,y\in\mathbb R$.
$$f(x+xy+f(y))=\left(f(x)+\frac12\right)\left(f(y)+\frac12\right)$$
for all $x,y\in\mathbb R$.