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Question

Mathematics Question on Inverse of a Function

The inverse of the function f(x)=exexex+ex+2f(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}+2 is given by

A

loge(x2x+2)12log_e(\frac{x-2}{x+2})^{\frac{1}{2}}

B

loge(x1x+1)12log_e(\frac{x-1}{x+1})^{\frac{1}{2}}

C

loge(1xx3)12log_e(\frac{1-x}{x*3})^{\frac{1}{2}}

D

loge(x1x+1)13log_e(\frac{x-1}{x+1})^{\frac{1}{3}}

Answer

loge(1xx3)12log_e(\frac{1-x}{x*3})^{\frac{1}{2}}

Explanation

Solution

The correct option is (C): loge(1xx3)12log_e(\frac{1-x}{x*3})^{\frac{1}{2}}