There is a cubic function with a leading coefficient of positive \(f(x) \). For function \(g(x) = e^{\(\sin \pi x)} - 1 \), a composite function \(h(x) = g(f(x)) \) defined in every set of real numbers. Both functions \(f(x) \) and the composite function \(h(x) = g(f(x)) \) are The conditions are satisfied. (a), (b): (a) The function \( h(x) \) has a local maximum value of 0 at \( x = 0 \). (b) In the open interval (0, 3), the number of different real roots of the equation h(z)=1 is 7. When if \(f(3) = 1/2 \) and \(f'(3) = 0 \), then \(f(2) = q/p \), find the value of \(p + q \, where p and q are coprime natural numbers.



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