Problem
ALG-B1-M12-P016 Variant 4, Problem 4
#16
★★★☆☆ Level 3 of 5
Find linear \(f\) such that \(f(f(x))=x+2\), \(f(0)>0\).
Let \(f(x)=ax+b\).
\(a^2=1\), \(b(a+1)=2\). Only \(a=1,b=1\) works. Answer: \(f(x)=x+1\).
Mock olympiad problem. Tags: linear-functions.