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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.)
Four derived restrictions | Comment 11 of 18 |
(In reply to re(2): A final input by Bractals)

A) The function must pass through (-1,-1), (0,0), (1,1)

B) If f(a)=b, f(b)=a for all a, b. (thus it is one-to-one and also f(f(a))=a)

C) For each point not on the line f(x)=x, if the slope of the line from it to the origin is b, then f(b)=1/b.

D) f(x)f(y)=f(xy) for all x, y (thus, f(x)^p=f(x^p) if p is an integer) 

  Posted by Gamer on 2006-12-30 01:56:55
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