Given the function f (x) = x2 + (a + 1) x + LG | a + 2 | (a ∈ R, and a ≠ - 2) (I) if f (x) can be expressed as the sum of an odd function g (x) and an even function H (x), find the analytic expressions of G (x) and H (x); (II) proposition p: the function f (x) is an increasing function in the interval [(a + 1) 2, + ∞); proposition q: the function g (x) is a decreasing function. If proposition p and Q have and only one is an increasing function Under the condition of (II), compare the size of F (2) and 3-lg2

Given the function f (x) = x2 + (a + 1) x + LG | a + 2 | (a ∈ R, and a ≠ - 2) (I) if f (x) can be expressed as the sum of an odd function g (x) and an even function H (x), find the analytic expressions of G (x) and H (x); (II) proposition p: the function f (x) is an increasing function in the interval [(a + 1) 2, + ∞); proposition q: the function g (x) is a decreasing function. If proposition p and Q have and only one is an increasing function Under the condition of (II), compare the size of F (2) and 3-lg2

(1) ∵ f (x) = g (x) + H (x), G (- x) = - G (x), H (- x) = H (x) ∵ f (- x) = - G (x) + H (x) = x2 + (a + 1) x + LG | a + 2 | - G (x) + H (x) = X2 - (a + 1) x + LG | a + 2 |, G (x) = x (a + 1) x, H (x) = x2 + LG | a + 2 | (II) ∵ function f (x) =