Spring 2016, problem 8
Find all continuous functions $f : \mathbf{R}\to\mathbf{R}$ such that $$f (f (x)) = f (x)+x,$$ for any $x\in \mathbf{R}$.
Find all continuous functions $f : \mathbf{R}\to\mathbf{R}$ such that $$f (f (x)) = f (x)+x,$$ for any $x\in \mathbf{R}$.