Group/Examples/inv x = 1 - x/Lemma 1

Lemma for Group Example: $x^{-1} = 1 - x$
Define $f: \openint 0 1 \to \R$ by:


 * $\map f x := \map \ln {\dfrac {1 - x} x}$

and $g: \R \to \openint 0 1$:


 * $\map g z := \dfrac 1 {1 + \exp z}$

Then:
 * $\map {f \circ g} x = x$