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 y is independent
In this case, think of equation 2 as being dependent on two variables. What makes this function interesting, is no matter what two real numbers you choose for x and y, that equation holds true. (You can choose whatever real x and y you want.)
The proof that f(0)=0 doesn't imply that x=y always, but it does for that part.
Posted by Gamer
on 2006-12-31 01:49:07