Chapter 7 Functions and Graphs

The Algebra of Functions 7.4 The Sum, Difference, Product, or Quotient of Two Functions Domains and Graphs

The Sum, Difference, Product, or Quotient of Two Functions Suppose that a is in the domain of two functions, f and g. The input a is paired with f(a) by f and with g(a) by g. The outputs can then be added to get f (a) + g(a).

The Algebra of Functions If f and g are functions and x is in the domain of both functions, then:

For find the following. a) (f + g)(4) b) (f – g)(x) c) (f /g)(x) d) Solution a) Since f (4) = –8 and g(4) = 13, we have ( f + g)(4) = f(4) + g(4) = –8 + 13 = 5.

d) Since f(–1) = –3 and g(–1) = –2, we have b) We have, c) We have, We assume d) Since f(–1) = –3 and g(–1) = –2, we have

Domains and Graphs we must first be able to find f (a) and g(a). This means a must be in the domain of both f and g.

Thus the domain of f + g, f – g, and find the domains of Solution The domain of f is The domain of g is all real numbers. Thus the domain of f + g, f – g, and

To find the domain of f /g, note that can not be evaluated if x + 1 = 0 or x – 2 = 0. Thus the domain of f /g is