Compositions of functions
Let g: A ?B and f: B ?C. The composition of f and g, denoted by
f o g, is the function from A to C defined by (f o g)(x) = f(g(x)).
Example: Let g: N ? N be defined by g(x)=x2. And let f: N ? N
--- (g o f)(x) = (2x)2 = 4x2
(f o f -1)(x) = f -1 (f(x)) = x;
(f -1 o f )(x) = f(f -1 (x)) = x.