Problem
ALG-B3-M11-P010 Square with a Coefficient
#10
★★★★★ Level 5 of 5
Let \(f:\mathbb Q\to\mathbb Q\) be additive and satisfy \(f(x^2)=2xf(x)\). Find \(f\).
Let \(f(x)=cx\).
We get \(cx^2=2c x^2\) for all \(x\), hence \(c=0\). The answer is \(f\equiv0\).
Mixed square condition.