Date: Oct 14, 2012 1:32 PM
Author: Edward
Subject: Defining "f o g" with Functions

So I've been learning about functions. Ideas such as one-to-one, onto, bijections....and so on. Things have been going smoothly and I've been going on my own through the text trying to do all of the exercises to prove to myself I understand the concepts on my own but I came into a problem where I don't know where to begin. I'm not really familiar with "g o f" and "f o g". Can somebody show me how to figure this out:

Let S = {1,2,3,4,5} and let T = {3,4,5,6,7}. Define function f : S --> T and g : S --> S as follows:
f = {(2,6), (1,7), (3,4), (5,3), (4,5) and
g = {(2,3), (1,2), (4,3), (5,5), (3,1)}.

(a.) Find "f o g" or explain why "f o g" is not defined, Repeat for "g o f", "f o f" and "g o g".
(b.) Which (if any) of f, g are one-to-one? Which (if any) are onto? Explain
(c.) Find f^-1 if it exists. If not explain why.
(d.) Find g^-1 if it exists. If not explain why.

*** ^ represents exponent ***

Anybody who understands these concepts better than I do?