Editing Möbius transformation (section)

=== Formula for the inverse transformation ===
The existence of the inverse Möbius transformation and its explicit formula are easily derived by the composition of the inverse functions of the simpler transformations. That is, define functions ''g''<sub>1</sub>, ''g''<sub>2</sub>, ''g''<sub>3</sub>, ''g''<sub>4</sub> such that each ''g<sub>i</sub>'' is the inverse of ''f<sub>i</sub>''. Then the composition
<math display="block">g_1\circ g_2\circ g_3\circ g_4 (z) = f^{-1}(z) = \frac{dz-b}{-cz+a}</math>
gives a formula for the inverse.