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 An Odd Function (Posted on 2006-12-28)
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 complicatedfunction and maybe you can help me with twoquestions.`
`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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