Given the function f (x) = loga (AX-1) (a > 0, a ≠ 1); (1) find the domain of definition of function f (x); (2) discuss the monotonicity of function f (x)

(1) From AX-1 ＞ 0, we get ax ＞ 1. (1 point) when a ＞ 1, X ＞ 0; (2 points) when 0 ＜ a ＜ 1, X ＜ 0. (3 points) so the domain of definition of F (x) is x ∈ (0, + ∞) when a ＞ 1; X ∈ (- ∞, 0) when 0 ＜ a ＜ 1. (4 points) (2) when a ＞ 1, let x1, X2 ∈ (0, + ∞)

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