Let \( g: R \rightarrow R \) be given by \( g(x)=e^{2 x}+3 x+\sin x+1 \). If \( g^{-1} \) is the...

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Let \( g: R \rightarrow R \) be given by \( g(x)=e^{2 x}+3 x+\sin x+1 \). If \( g^{-1} \) is the inverse function of \( g \), then the value of \( \frac{1}{\left(g^{-1}\right)^{\prime}(2)} \) is
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