1. Chapter 7
Functions and Graphs

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

3. 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).

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

5. 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.

6. 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

7. 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.

8. 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

9. 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