Look at the two functions and . The question is how the composed functions you can create by using these two functions look like. To get an idea, first simplify the expressions for the composed functions f°f, g°g, f°g, g°f, f°g°f, g°f°g, f°g°f°g, and g°f°g°f. (You should also describe in your paper why no parantheses are needed here). Then show that there are only a limited number of functions you can get by repeatedly composing functions f and g. What is the reason for that?
Erich Prisner, August 2003