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
(In reply to Almost there?
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.