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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.)
problem with expression (1) | Comment 15 of 18 |

Why in (1)  f(0) = f(0f(0)) = 0f(0) = 0 ?

    


  Posted by Ferdinand on 2006-12-30 18:10:07
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