Problem
ALG-B3-M09-P009 Order Preservation
#9
★★★☆☆ Level 3 of 5
Let \(f\) be additive, strictly order-preserving \(x
Order preservation means strict monotonicity.
The function is strictly increasing and additive, hence linear: \(f(x)=cx\). From \(f(1)=1\), \(c=1\). The answer is \(f(x)=x\).
Order preservation as regularity.