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
re(3): A final input by JLo)
I realized after my post that there was
a problem. I am working on a more complicated
function and maybe you can help me with two
questions.
1) Let x>0. Does the following exist?
max { 2^i*3*j  i,j in Z and 2^i*3^j <= x }
2) If the answer to 1) is yes.
Let x,y>0. If
2^m*3^n = max { 2^i*3*j  i,j in Z and 2^i*3^j <= x }
and
2^p*3^q = max { 2^i*3*j  i,j in Z and 2^i*3^j <= y }
does
2^(m+p)*3^(n+q) = max { 2^i*3*j  i,j in Z and 2^i*3^j <= xy } ?

Posted by Bractals
on 20061230 11:46:27 