FKMO 1997 Problem 3

Find all pairs of functions $f, g: \mathbb R \to \mathbb R$ such that [list] (i) if $x < y$ , then $f(x) < f(y)$ ;

(ii) $f(xy) = g(y)f(x) + f(y)$ for all $x, y \in \mathbb R$ . [/list]