Cute geometry problem

Geometry Level pending

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 $$f(B)$$.

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