Let f:R→R satisfy
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f(a)≠0 for some a in R
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f(xf(y))=yf(x) for all x,y in R
Prove that f(-x)=-f(x) for all x in R.
(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)
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Posted by Gamer
on 2006-12-30 01:56:55 |
Four derived restrictions
