Given the function f (x) = (1 / 3) ^ x, X belongs to [- 1,1], the minimum value of function g (x) = [f (x)] ^ 2-2af (x) + 3 is h (a) (1) When a ＞ = 1, find H (a) (2) Whether there is a real number m, while satisfying 1: M > n > 3,2: when the definition field of H (a) [n, M], whether the value field [n ^ 2, m ^ 2] exists, if it exists, find out the value of M, N, if it does not exist, explain the reason

Given the function f (x) = (1 / 3) ^ x, X belongs to [- 1,1], the minimum value of function g (x) = [f (x)] ^ 2-2af (x) + 3 is h (a) (1) When a ＞ = 1, find H (a) (2) Whether there is a real number m, while satisfying 1: M > n > 3,2: when the definition field of H (a) [n, M], whether the value field [n ^ 2, m ^ 2] exists, if it exists, find out the value of M, N, if it does not exist, explain the reason

(1) Firstly, we find that the range of F (x) is [1 / 3,3] g (x) = (f (x) - a) ^ 2 + 3-A ^ 2, which is a quadratic function with opening upward and symmetry axis of F (x) = A. then, if a is in the definition domain of this function [1 / 3,3], when f (x) = a, G (x) is the smallest, that is, 1n > 3, and when the definition domain of H (a) [n, M], we can know from (1) that h (a) = 12-6ah (a) is simple