Let f and g be functions with domains A and B. Then the
functions f + g, f – g, fg, and f/g are
defined as fol lows :
Given two function f and g, the composite function
f o g (also called the composition of f and
g) is defined by ( f o g)(x) = f (g(x)) .
The domain of f o g is the set of all x in the domain of g
such that g(x) is in the domain of f.
Example 1: Find f + g, f – g, fg, and f/g and their
domains.
Example 2: For f(x) = 3x – 5 and g(x) = 1 – x2,
evaluate the following.
Example 3: Find the functions f o g , g o f , f o f , g o
g , and f o g o h , and their domains.
Example 4: Ex press the function 
in
the form f o g o h .
