College Algebra 9th txtbk

224 CHAPTER 3 FUNCTIONS
Z DEFINITION 1 Operations on Functions
The sum, difference, product, and quotient of the functions f and g are the
functions defined by
( f g)(x) f(x) g(x)
( f g)(x) f(x) g(x)
( fg)(x) f(x)g(x)
a f f(x)
b(x)
g g(x)
g(x) 0
Sum function
Difference function
Product function
Quotient function
The domain of each function consists of all elements in the domains of both f and
g, with the exception that the values of x where g(x) 0 must be excluded from
the domain of the quotient function.
ZZZ EXPLORE-DISCUSS 1
The following activities refer to the graphs of f and g shown in Figure 1 and the
corresponding points on the graph shown in Table 1.
( f g)(x) (A) (B) (C) ( fg)(x) (D) a f g b(x)
Table 1
y
x f(x) g(x)
10
y f(x)
0 8 0
2 7 2
y g(x)
4 6 3
6 5 3
10
x
8 4 2
Z Figure 1
10 3 0
For each of the following functions, construct a table of values, sketch a graph,
and state the domain and range.
EXAMPLE 1
Finding the Sum, Difference, Product, and Quotient Functions
Let f (x) 14 x and g(x) 13 x. Find the functions f g, f g, fg, and fg, and
find their domains.
SOLUTION
( f g)(x) f (x) g(x) 14 x 13 x
( f g)(x) f (x) g(x) 14 x 13 x
( fg)(x) f (x)g(x) 14 x 13 x
1(4 x)(3 x)
212 x x 2
a f f (x)
b(x)
g g(x) 14 x
13 x 4 x
A 3 x