Let \( f(x) \) be a real valued function such that \( f(x)=\frac{2 x-1}{x-2} \forall x \in \) \(...

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Let \( f(x) \) be a real valued function such that \( f(x)=\frac{2 x-1}{x-2} \forall x \in \) \( (2, \infty) \) and \( g(x)=\frac{x^{2}+1}{x}+\frac{(f(x))^{2}+1}{f(x)} \forall x2 \), then minimum value of \( g(x) \) is
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