It is known that the image of function f (x) and the image of function H (x) = 1 / 3x ^ 3 + x ^ 2 + 2 are symmetric with respect to a (0,1) (1) Find the analytic expression of F (x); (2) If G (x) = f (x) + ax, and G (x) is an increasing function on (- ∞, + ∞), find the value range of real number a~ Mathematics is not very good. In fact, the first problem is how to find the symmetry of cubic function,

It is known that the image of function f (x) and the image of function H (x) = 1 / 3x ^ 3 + x ^ 2 + 2 are symmetric with respect to a (0,1) (1) Find the analytic expression of F (x); (2) If G (x) = f (x) + ax, and G (x) is an increasing function on (- ∞, + ∞), find the value range of real number a~ Mathematics is not very good. In fact, the first problem is how to find the symmetry of cubic function,

(1) From the symmetry of F (x) and H (x) with respect to (1,0), f (x) = - H (- x + 2) - x + 2 is obtained from the symmetry of x = 1; - H (x) is obtained from the symmetry of y = 0; substituting f (x) = - (1 / 3 (- x + 2) ^ 3 + (- x + 2) ^ 2 + 2); (2) g (x) = f (x) + AX = (1 / 3) x & # 179; - X & # 178; + ax is an increasing function in R -- > G '(x) = 3x & # 178; -