Problem
ALG-B3-M03-P002 Constant shift
#2
★★☆☆☆ Level 2 of 5
Let \(f:\mathbb Q\to\mathbb Q\), \(f(x+y)=f(x)+f(y)-1\), \(f(2)=7\). Find \(f\).
Hint. Put \(g(x)=f(x)-1\).
Then \(g\) is additive and \(g(2)=6\), so \(g(1)=3\). Hence \(g(q)=3q\), and \(f(q)=3q+1\).
Goal: show which conditions actually force a function to be linear or affine.