Given that the sum of the maximum and minimum value of the function y = ax (A & gt; 0 and a ≠ 1) on [1,2] is 20, Let f (x) = ax + 2. (1) find the value of a; (2) prove that: F (x) + f (1-x) = 1; (3) find f (12013) + F (22013) + F (32013) + +F (20102013) + F (20112013) + F (20122013)

Given that the sum of the maximum and minimum value of the function y = ax (A & gt; 0 and a ≠ 1) on [1,2] is 20, Let f (x) = ax + 2. (1) find the value of a; (2) prove that: F (x) + f (1-x) = 1; (3) find f (12013) + F (22013) + F (32013) + +F (20102013) + F (20112013) + F (20122013)

(1) When ∵ y = ax (A & gt; 0 and a ≠ 1), the sum of the maximum and the minimum on [1,2] is 20, when ∵ A & gt; 1, A2 + a = 20, the solution is a = 4, 1 & gt; a & gt; 0, a + A2 = 20, there is no solution