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An Odd Function (Posted on 2006-12-28) Difficulty: 3 of 5
Let f:R→R satisfy
  1. f(a)≠0 for some a in R
  2. f(xf(y))=yf(x) for all x,y in R
Prove that f(-x)=-f(x) for all x in R.

See The Solution Submitted by Bractals    
Rating: 3.8333 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(4): A final input | Comment 14 of 18 |
(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 2006-12-30 11:46:27
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