I think I've figured out (a):
f(a) = b; f(b) = a; f(c) = b, so
f(f) = {(b, a), (a, b), (b, a)}, and
f(f(f)) = {(a, b), (b, a), (c, a)}
But I'd love for someone to confirm this.
I'm still having trouble with part (b) also. Thanks for any help!
I've come across a challenging problem in my test review:
Given f = {(a, b), (b, a), (c, b)}, a function from X = {a, b, c} to X:
(a) Write f o f and f o f o f as sets of ordered pairs.
(b) Define f^n = f o f o ... o f to be the n-fold composition of f with itself. Write f^9 and f^623 as sets of ordered pairs.
I have no idea how to approach this. I know that f o f and f o f o f are f(f) and f(f(f)), but I can't see how I can compose that. Where in f can I insert f? Part (b) also looks daunting.
Any help would be appreciated!