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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    
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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


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

  Posted by Steve Herman on 2015-10-14 11:13:01
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