Cute geometry problem
Let \(a,b\in \mathbb R\). For a point \(P = (x,y) \in \mathbb R^2 \) define \(f(P) = ax+by\). Suppose the line \(ax+by = 4\) intersects the line segment joining two points \(A\) and \(B\) in the plane at a point \(C\) usch that \(AC = 2\cdot CB\). If \(f(A) = 3\), find \(f(B)\).