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 re: Almost there?
by Steve Herman)
Sorry if I skipped some steps.
1) Suppose f(2)=a, then f(f(2))=f(a)=2
we have a^2-2=a
solutions a=2 or a=-1
So either f(2)=2 or f(2)=-1
2) f(-2)=2 because f(f(f(-2)))=f(f(x)) which implies x^2-2=2
so x=2 (case 1)
or x=-2 (case 2) ***I may have made an error here***
Posted by Jer
on 2015-10-14 10:07:48