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

Home > Just Math
Function Existence Exercise (Posted on 2015-10-11) Difficulty: 3 of 5
R denotes the set of real numbers. Does there exist functions F: R → R such that:
F(F(x)) = x2 - 2?
If so, find all such functions.
If not, prove that no such function can exist.

Source: American Mathematical Monthly

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Almost there? Comment 4 of 4 |
(In reply to re: Almost there? by Steve Herman)

Ah, very clever.


I agree that either 

(a) f(2) = 2 and f(-1) = -1

or

(b) f(2) = -1 and f(-1) = 2

  Posted by Steve Herman on 2015-10-14 11:13:01
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information