A certain function \(f\) has the properties that \(f(3x) = 3f(x)\) for all positive real values of \(x\), and that \(f(x) = 1 - |x - 2|\) for \(1\leq x \leq 3\). Find the smallest \(x\) for which \(f(x) = f(2001)\).

(第十九届AIME2 2001 第8题)