Cosider the functions f and g defined as follows.
f(x) = x-3/x-2 for all x E R, does not equal 2.
g(x) = 3-x for all x E R.
Find all possible functions that are generated by composing the functions f and g. After finding all functions, prove that you have them all and identify the domain of each. You will want to look at (f of g), g of f, f of f, g of g, f of(g of f) and so on.