Problem
ALG-B3-M02-P007 Symmetric difference
#7
★★★★☆ Level 4 of 5
Find all \(f:\mathbb R\to\mathbb R\) such that \(f(x+y)=f(x-y)+4y\) for all \(x,y\in\mathbb R\).
Hint. Take \(x=y\).
With \(x=y\), \(f(2y)=f(0)+4y\). Thus for every \(t\), \(f(t)=f(0)+2t\). Check: \(f(x+y)=f(0)+2x+2y=f(0)+2x-2y+4y=f(x-y)+4y\).
Goal: choose the right first substitution and then verify the found function.