Suppose \(f(x),g(x)\) and \(h(x)\) are polynomials such that

\[\large |f(x)|-|g(x)|+|h(x)|=\begin{cases} -1,\quad \text{if } x<-1\\ 3x+2,\quad \text{if } -1 \leq x \leq 0\\ -2x+2,\quad \text{if } x>0 \end{cases}\\ \]

Find the value of \(g(2)\).

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