Problem
ALG-B1-M12-P028 Variant 7, Problem 4
#28
★★★★★ Level 5 of 5
Increasing \(f:\mathbb R\to\mathbb R\), \(f(x+f(y))=f(x)+y\). Find \(f\).
First \(y=0\), then \(x=0\).
\(f(0)=0\), \(f(f(y))=y\). Putting \(y=f(t)\), we get additivity. An increasing additive function is \(cx\); from \(c^2=1\) and increasing, \(c=1\). Answer \(f(x)=x\).
Mock olympiad problem. Tags: functional-equation.