Problem
ALG-B3-M03-P003 Constancy
#3
★★☆☆☆ Level 2 of 5
Find all \(f:\mathbb R\to\mathbb R\) such that \(f(x+y)=f(x)\) for all \(x,y\in\mathbb R\).
Hint. Take \(x=0\).
With \(x=0\), \(f(y)=f(0)\) for all \(y\). Every constant function works.
Goal: show which conditions actually force a function to be linear or affine.