Problem
ALG-B1-M11-P010 Additivity
#10
★★☆☆☆ Level 2 of 5
Let \(f:\mathbb Q\to\mathbb Q\), \(f(x+y)=f(x)+f(y)\), \(f(5)=20\). Find \(f\left(\frac{3}{2}\right)\).
Find \(f(1)\).
\(5f(1)=20\), so \(f(1)=4\). Therefore \(f(q)=4q\), and \(f\left(\frac{3}{2}\right)=6\).
Strategy: the domain \(\mathbb Q\) lets us fully solve Cauchy.