Let the function \(f:[1,\infin)β\R\) be defined by
\(f(t) = \begin{cases} (-1)^{n+1}2, & \text{if } t=2n-1,n\in\N, \\ \frac{(2n+1-t)}{2}f(2n-1)+\frac{(t-(2n-1))}{2}f(2n+1) & \text{if } 2n-1<t<2n+1,n\in\N. \end{cases}\)
Define \(g(x)=\int\limits_{1}^{x}f(t)dt,x\in(1,\infin).\) Let Ξ± denote the number of solutions of the equation g(x) = 0 in the interval (1, 8] and \(Ξ²=\lim\limits_{xβ1+}\frac{g(x)}{x-1}\). Then the value of Ξ± + Ξ² is equal to _____.