0-6: Operations on and Composition of Functions Objectives: Define the sum, difference, product, quotient and composition of functions ©2002 Roy L. Gover (roygover@att.net)

Operations Given: Sum: Domain: Difference: Domain:

Operations cont . Product: Domain: Quotient: Domain:

Example Example: Given f and g as follows: Find each of the following and determine the domain of the resulting function. a.) (f + g)(x) b.) (f - g)(x) c.) (f · g)(x) d.) (f / g)(x)

Composition Given: Two function f and g, the composite function, is defined by: The domain of f g is the set of all numbers x in the domain of g such that g(x) is in the domain of f. o

Example Example: Given the functions f and g, find f ○ g and the domain of f ○ g.