>>13657177We can form a sequence: {f(x), f(ax), f(a^2 x), ... }; this is a constant sequence since f(x)=f(ax), so the limit is f(x) (or any other term we choose).
On the other hand, lim a^n = 0 since |a| < 1. f is continuous, so lim f(a^n) = f(lim a^n) = f(0).
Thus, lim f(a^n) equals both f(x) and f(0). So any f(x) has the same value as f(0); f is constant.
