Answer by Jyrki Lahtonen for What causes a set of functions to form a group...
This is a famous example of a finite group of linear fractional transformations. These are transformations ofthe form$$x\mapsto \frac{ax+b}{cx+d},$$wher $ad-bc\neq0$. The use of the term "linear...
View ArticleWhat causes a set of functions to form a group under composition?
In my textbook the following functions are given and are said to form a group under composition:$f_1(x) = x$, $f_2(x) = \frac{1}{x}$, $f_3(x) = 1-x$, $f_4(x) = \frac{1}{1-x}$, $f_5(x) = \frac{x-1}{x}$,...
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