Problem
ALG-B3-M03-P001 Rational additivity
#1
★★☆☆☆ Level 2 of 5
Let \(f:\mathbb Q\to\mathbb Q\), \(f(x+y)=f(x)+f(y)\), \(f(1)=5\). Find \(f(q)\).
Hint. First find \(f(n)\), then \(f(m/n)\).
For integers \(n\), \(f(n)=5n\). If \(q=m/n\), then \(n f(q)=f(m)=5m\), so \(f(q)=5q\).
Goal: show which conditions actually force a function to be linear or affine.