（为方便起见，用英文叙述）
下面是对 g(x)=f(f(x)) = x^2-x+1 求 f(1), f(0) 一题以及由其引发之讨论，本着从特殊到一般的思路之总结，请KDE235大师以及各位大师过目指正，总结得是否到位和正确, 尤其是结论6。
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For x belong to domain X and for a given single valued function g(x) on G (X to G is an injective mapping), define f(x) so that f(f(x))=g(x);
Name such defined f(x) as the square root function of g(x), then the following statements are true:
1. f(x) exists
2. f(x) is a single valued function of x
3. f(g(x))=g(f(x))
4. If the set for all possible values of f(x) is F, then F <=G
5. Both g(x) and f(x) have their own inverse functions.
6. For a given pair of x_p and x_q (>x_p) in X,
then the following sequence forms an equivalent class of [x_p, x_q] on domain X:
a(1)=g(x_p); a(2)=g(x_q)
a(i+2)=g(a(i)) for i =1 to infinity (1)
Then the below defined function f(x) is the square root function of g(x), designate as g^1/2 (x)
f(x) = g^(1/2) (x) such that f(aj)=a(j+1) (a(i) defined in (1) for j=1 to infinity)
