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Tags: function, algebra, functional equation, algebra unsolved



Find all functions $f : \mathbb R \to \mathbb R$ such that \[f\left(x+xy+f(y)\right)= \left( f(x)+\frac 12 \right) \left( f(y)+\frac 12 \right) \qquad \forall x,y \in \mathbb R.\]