Let the function f : [1, ∞) → ℝ be defined by f(2n − 1) = (−1)^(n+1)2 for n ∈ ℕ, and, if 2n − 1 < t < 2n + 1, by f(t) = {(2n + 1 − t)/2}f(2n − 1) + {(t − (2n − 1))/2}f(2n + 1). Define g(x) = ∫₁ˣ f(t)dt, x ∈ (1, ∞). Let α denote the number of solutions of g(x) = 0 in the interval (1, 8] and β = lim[x→1⁺] g(x)/(x − 1). Then the value of α + β is equal to ________.