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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: Almost there? | Comment 2 of 4 |
(In reply to Almost there? by Jer)

Jer:


I am not sure that I agree with any of this.

1) Just because f(f(2)) = 2, I don't think it follows that f(2) = 2.
    For instance, if g(g(x)) = x 
      then g(x) could be 1/x if x <> 0 and 0 if x = 0.

2) Even if f(f(f(0))) = 2 (which I don't think is necessarily true), I don't see that it follows that f(0) = 2.

Steve

  Posted by Steve Herman on 2015-10-13 14:36:23
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