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Some other kind of root extraction (Posted on 2006-11-07) Difficulty: 4 of 5
Let's call a real-valued continuous function an n-th identity root when it generates the identity function after exactly n compositions with itself. For example f(x)=-x is a 2nd identity root because f(f(x))=x.

1. The function f(x)=1-1/x is a 3rd identity root. Unfortunately it is undefined at x=0. Are there identity roots for n>2 which are defined for all real numbers?

2. For a given real number c and n>1, give an example of an n-th identity root which is defined for all real numbers except c. How many such roots exist?

See The Solution Submitted by JLo    
Rating: 4.0000 (3 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): CuriousJLo2006-11-10 08:36:32
re: CuriousRichard2006-11-09 18:15:56
re: CuriousJoel2006-11-09 16:38:51
QuestionCuriousJLo2006-11-09 15:39:48
Any n, one cRichard2006-11-08 23:48:05
re: There's still something to find...Joel2006-11-08 19:26:41
Some ThoughtsA complex answere.g.2006-11-08 19:10:57
Hints/TipsThere's still something to find...JLo2006-11-08 17:43:45
SolutionsolutionJoel2006-11-07 20:33:02
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