It is known that a set M is a set of all functions f (x) which satisfy the following properties: for function f (x), any two different independent variables X1 and X2 in the domain of definition have | f (x1) - f (x2) | ≤| x1-x2 | (1) judge whether the function f (x) = 3x + 1 belongs to set M? (2) if G (x) = a (x + 1 x) belongs to m on (1, + ∞), find the value range of real number a

It is known that a set M is a set of all functions f (x) which satisfy the following properties: for function f (x), any two different independent variables X1 and X2 in the domain of definition have | f (x1) - f (x2) | ≤| x1-x2 | (1) judge whether the function f (x) = 3x + 1 belongs to set M? (2) if G (x) = a (x + 1 x) belongs to m on (1, + ∞), find the value range of real number a

(1) As an example, if x = 1, X2 = 2, then f (x1) = 4, f (x1) = 4, f (x1) = 4, f (x2) = 7, and 124; f (x1) - f (x1) - f (x2) | f (x1) - f (x1) - f (x2) | = 3 ≤ 1 = | 3x-1-1 ∉ m, we can give an example: if x = 1 = 1, X2 = 2, then f (x1 = 4, f (x1) = 4, f (x1) = 4, f (f (x1) = 4, f (f (x1) = 4, f (x1 = 4, f (x1) = 4, f (x1 = 4, f (x1) = 4, f (x (x1) - G (g (x1) - G (x1) - G (x2) - G (x2) - G (x (x2) | g (x) - G (x2) - G (x2))