Problem
ALG-B3-M09-P002 Boundedness on a Segment
#2
★★☆☆☆ Level 2 of 5
Let \(f\) be additive, \(|f(x)|\le5\) for \(0\le x\le1\), and \(f(1)=3\). Find \(f\).
Boundedness on an interval gives continuity.
An additive function bounded on an interval is continuous. Therefore \(f(x)=cx\). From \(f(1)=3\), we get \(f(x)=3x\).
Important standard fact.