Fall 2018, problem 71
Find all functions $f:\mathbb{R}\to\mathbb{R}$ that satisfy the condition
$\displaystyle\qquad f\left(f\left(x\right)+y\right)=2x+f\left(f\left(y\right)-x\right) \quad\text{for all }x,y\in\mathbb{R}$.
Find all functions $f:\mathbb{R}\to\mathbb{R}$ that satisfy the condition
$\displaystyle\qquad f\left(f\left(x\right)+y\right)=2x+f\left(f\left(y\right)-x\right) \quad\text{for all }x,y\in\mathbb{R}$.