Problem
ALG-B3-M10-P003 Square of the Value
#3
★★★★☆ Level 4 of 5
Find all additive \(f:\mathbb Q\to\mathbb Q\) such that \(f(x^2)=f(x)^2\).
On \(\mathbb Q\): \(f(x)=cx\).
Let \(f(x)=cx\). Then \(cx^2=c^2x^2\) for all \(x\). We get \(c=0\) or \(c=1\). The answer is \(f\equiv0\), \(f(x)=x\).
The zero answer is part of the system.