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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(2): A final input | Comment 6 of 18 |
(In reply to re: A final input by JLo)

Could you give me your proof , in detail, for

If x outside {-1,0,1}, then f(x)=x or f(x)=1/x.


  Posted by Bractals on 2006-12-29 21:28:17
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