It is known that f (x) is a linear function, and 4f (1-x) - 2F (x-1) = 3x + 18 (1) Find the maximum value of function f (x) on [- 1,1], and compare the size of F (2007) and f (2008) (2) Can you solve the problem (1) without seeking the analytic expression of F (x) (3) Remove the condition that "f (x) is a linear function",

It is known that f (x) is a linear function, and 4f (1-x) - 2F (x-1) = 3x + 18 (1) Find the maximum value of function f (x) on [- 1,1], and compare the size of F (2007) and f (2008) (2) Can you solve the problem (1) without seeking the analytic expression of F (x) (3) Remove the condition that "f (x) is a linear function",

(1) Let f (x) = ax + B
Then 4 * (a (1-x) + b) - 2 (a (x-1) + b) = 3x + 18
Simplification: - 6AX + 6A + 2B = 3x + 18
The corresponding coefficient is equal: a = - 0.5, B = 10.5, the rest is simple
(2) Because it is a function, the maximum value can be compared with the size of the two ends at the endpoint
(3) No way