Problem
ALG-B3-M11-P002 Square of Iteration
#2
★★★★☆ Level 4 of 5
Find all additive \(f:\mathbb Q\to\mathbb Q\) if \(f(f(x))=9x\).
Let \(f(x)=cx\).
Then \(c^2x=9x\), so \(c=3\) or \(c=-3\). The answers are \(f(x)=3x\), \(f(x)=-3x\).
Short rational iteration.