1. f(a)≠0 for some a in R
2. f(xf(y))=yf(x) for all x,y in R

Note that b does not take on all real numbers, just those where f(a)=ab for some a. Thus, for these b, f(b)=1/b.

It is also true that f(x)f(y)=f(xy); f(f(x)*f(y))=y*f(f(x)) which means f(f(x)*f(y))=xy, and f(x)f(y)=f(xy)