Let f:R→R satisfy

f(a)≠0 for some a in R

f(xf(y))=yf(x) for all x,y in R
Prove that f(x)=f(x) for all x in R.
(In reply to
problem with expression (1) by Ferdinand)
Substituting x=0 and y=0 gives f(0*f(0))=0*f(0) by condition 2.
We don't know what f(0) is yet, but it's clear that anything it could be times 0 must be 0. So it reduces to f(0)=0.

Posted by Gamer
on 20061230 18:55:12 