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Derivative of an Inverse Function

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Let ff be a one-to-one function defined by f(x)=ex+xf(x)=e^{x}+x. If g(x)=f−1(x)g(x)=f^{-1}(x), what is the value of g′(f(0))g'(f(0))?

A

11

B

1e0\frac{1}{e^{0}}

C

12\frac{1}{2}

D

1e+1\frac{1}{e+1}

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