ZA-SAMO 1999 Problem 5

Let $S$ be the set of all rational numbers whose denominators are powers of 3. Let $a$ , $b$ and $c$ be given non-zero real numbers. Determine all real-valued functions $f$ that are defined for $x \in S$ , satisfy $$f(x) = af(3x) + bf(3x - 1) + cf(3x - 2) \textrm{ if }0 \leq x \leq 1,$$ and are zero elsewhere.