Basic Function Concepts 197
Solution
a. y
x
=
−
3
1
Step 1. Set the denominator equal to 0 and solve for x.
x − 1 = 0
x − 1 + 1 = 0 + 1
x= 1
Step 2. State the domain.
The domain of y
x
=
−
3
1
is all real numbers except 1.
b. yxx−^25 +
Step 1. Because the square root is an even root, set the term under the rad-
ical greater than or equal to 0 and solve the inequality.
x− 20 ≥
x− 22 + ≥ 02 +
x≥ 2
Step 2. State the domain.
The domain of yxx− 25 + is all real numbers greater than or
equal to 2.
Terminology of Functions
A function is completely determined when the domain is known and the
rule is specifi ed. Even though the range is determined, it is often diffi cult to
exhibit or specify the set of numbers in the range. Some of the techniques
for determining the range of a function are beyond the scope of this book,
and the focus here will be mostly on the domain and the equation that gives
the rule. In fact, the words rule and equation will be used synonymously.
Some common terminology used in the study of functions is the follow-
ing: (1) Domain values are called inputs, and range values are called outputs.
(2) In equations of the form y = 3 x + 5, x is called the independent vari-
able, and y is called the dependent variable. Also, a convenient notation for
a function is to use the symbol f(x) to denote the value of the function f at a
