# 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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