A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x....

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A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x, y \in R, f(0) \neq 1 \),
\( \mathrm{P} \)
\( f^{\prime}(0)=\mathrm{e} \) and \( g \) be the inverse of \( f \).

The value of \( g^{\prime \prime}(e) \) is equal to :
(1) \( -\frac{2}{e^{2}} \)
(2) \( -\frac{1}{2 e^{2}} \)
(3) \( -2 \mathrm{e}^{2} \)
(4) \( -\frac{2}{e^{3}} \)


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