Problem
ALG-B3-M09-P001 Increasing Additivity
#1
★★☆☆☆ Level 2 of 5
Let \(f:\mathbb R\to\mathbb R\) be additive, increasing, and \(f(1)=4\). Find \(f\).
A monotone additive function is linear.
Since \(f\) is increasing and additive, \(f(x)=cx\). From \(f(1)=4\), \(c=4\). The answer is \(f(x)=4x\).
Basic regularity task.