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
A final input by Gamer)
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)

Posted by Gamer
on 20061230 00:01:06 