perplexus.info :: Just Math : Function Existence Exercise

Function Existence Exercise (Posted on 2015-10-11)

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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