MAT103

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 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?