Sullivan Algebra and Trigonometry: Section 3.5 Objectives Form the Sum, Difference, Product, and Quotient of Two Functions Form the Composite Function and Find Its Domain

(f + g)(x) = f(x) + g(x). (f - g)(x) = f(x) - g(x). If f and g are functions, their sum f + g is the function given by (f + g)(x) = f(x) + g(x). The domain of f + g consists of the numbers x that are in the domain of f and in the domain of g. If f and g are functions, their difference f - g is the function given by (f - g)(x) = f(x) - g(x). The domain of f - g consists of the numbers x that are in the domain of f and in the domain of g.

Their product is the function given by The domain of consists of the numbers x that are in the domain of f and in the domain of g. Their quotient f / g is the function given by The domain of f / g consists of the numbers x for which g(x) 0 that are in the domain of f and in the domain of g.

Example: Define the functions f and g as follows: Find each of the following and determine the domain of the resulting function. a.) (f + g)(x) = f(x) + g(x)

b.) (f + g)(x) = f(x) + g(x) c.) ( )(x) = f(x)g(x)

d.) We must exclude x = - 4 and x = 4 from the domain since g(x) = 0 when x = 4 or - 4.

Given two function f and g, the composite function, denoted by f g (read as “f composed with g”) is defined by o 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: Given the functions f and g, find (f g)(2)

o o Example: Given the functions f and g, find the domain of f g. The domain of f g consists of those x in the domain of g, thus, x = - 2 is not in the domain of the composite function. o Furthermore, the domain of f requires that So:

Example: Given the functions f and g, find f g.