Domain of 'fog'

Algebra Level pending

Domain of \( f(g(z)) \) where \( f(z)=\frac{1}{z^{2}-1} \) and \( g(z)= \frac{1}{z} \) is the set of Complex numbers except few of them.

Let \(P\) be their product and \(S\) be their sum. What is \(S+P+1\) ?

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