Composite Function?

Let g be the function on the set { a, b, c } defined by g(a) = b, g(b) = c and g(c) = a.





Let f be the function from the set { a, b, c } to the set { 1, 2, 3 } such that f(a) = 3, f(b) = 2 and f(c) = 1.





What is the composite function fg and gf?





Please do show your workings clearly and explain...I have trouble doing this type of question...Thank you!! =D

Composite Function?
In mathematics, a composite function, formed by the composition of one function on another, represents the application of the former to the result of the application of the latter to the argument of the composite. The functions f: X → Y and g: Y → Z can be composed by first applying f to an argument x and then applying g to the result. Thus one obtains a function g o f: X → Z defined by (g o f)(x) = g(f(x)) for all x in X. The notation g o f is read as "g circle f", or "g composed with f", "g following f", or just "g of f".


http://en.wikipedia.org/wiki/Function_co...





gf is undefined because g is undefined on the set { 1, 2, 3 }


fg is simply f(g(x)) ie: g(a) = b, f(b) = 2 therefore fg(a) = 2