Let f (x) be a function defined on R with period 2. In the interval [- 1, 1], f (x) = ax + 1, − 1 ≤ x < 0 & nbsp; & nbsp; & nbsp; BX + 2x + 1, 0 ≤ x ≤ 1, where a, B ∈ R. if f (12) = f (32), then the value of a + 3b is______ ．

Let f (x) be a function defined on R with period 2. In the interval [- 1, 1], f (x) = ax + 1, − 1 ≤ x < 0 & nbsp; & nbsp; & nbsp; BX + 2x + 1, 0 ≤ x ≤ 1, where a, B ∈ R. if f (12) = f (32), then the value of a + 3b is______ ．

∵ f (x) is a function defined on R with period 2, f (x) = ax + 1, − 1 ≤ x ＜ 0 & nbsp; & nbsp; & nbsp; BX + 2x + 1, 0 ≤ x ≤ 1, ∵ f (32) = f (- 12) = 1-12a, f (12) = B + 43; f (12) = f (32), ∵ 1-12a = B + 43; ① f (- 1) = f (1), ∵ 2A + B = 0, ② from ① to ②

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