All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Some other kind of root extraction (Posted on 2006-11-07)
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)

 Subject Author Date re(2): Curious JLo 2006-11-10 08:36:32 re: Curious Richard 2006-11-09 18:15:56 re: Curious Joel 2006-11-09 16:38:51 Curious JLo 2006-11-09 15:39:48 Any n, one c Richard 2006-11-08 23:48:05 re: There's still something to find... Joel 2006-11-08 19:26:41 A complex answer e.g. 2006-11-08 19:10:57 There's still something to find... JLo 2006-11-08 17:43:45 solution Joel 2006-11-07 20:33:02

 Search: Search body:
Forums (0)