Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises - Page 452: 26

$y=-ln\frac{(1-x)}{(1+x)}$

Given: $y=\frac{1-e^{-x}}{1+e^{-x}}$ Now, replace the terms to find out the value of inverse function. Replace x with y $x=\frac{1-e^{-y}}{1+e^{-y}}$ $e^{-y}=\frac{1-x}{1+x}$ Hence, $y=-ln\frac{(1-x)}{(1+x)}$