Franklin College
Erich Prisner

Writing Project 19:

Composition of Functions I

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 ff, gg, fg, gf, fgf, gfg, fgfg, and gfgf. (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