Problem
ALG-B3-M03-P005 Affine equation
#5
★★★☆☆ Level 3 of 5
Let \(f:\mathbb Q\to\mathbb Q\), \(f(x+y)=f(x)+f(y)-f(0)\), \(f(0)=4\), \(f(1)=9\). Find \(f\).
Hint. Subtract \(f(0)\).
Let \(g(x)=f(x)-4\). Then \(g(x+y)=g(x)+g(y)\), and \(g(1)=5\). On \(\mathbb Q\), \(g(q)=5q\), so \(f(q)=5q+4\).
Goal: show which conditions actually force a function to be linear or affine.