Carson Elementary And Intermediate Algebra 3e Page 2
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Carson Elementary and Intermediate Algebra 3e
Section 10.1
Example 1:
49
3
a.
7
e.
27
3
3
b.
25
= not a real number
f.
125
5
5
c.
100
10
g.
32
2
d.
100
10
64
4
3
h.
125
5
2. Evaluate radical functions.
Radical functions are functions that have a polynomial as the radicand. They are evaluated the same as
the linear functions we did earlier. Substitute the given value for the variable in the function.
Example 2:
f
x
3
x
2
f
3
3
3
2
11
f
5
3
5
2
13
Not a real number
3. Find the domain of radical functions.
The even root of a negative number does not exist so we must be careful to use only numbers that make
the radicand be 0 or positive. In Example 2, what numbers can be put in for x, so that the result will be a
real number?
Since the index is even, so the radicand (3x + 2) must be greater than or equal to 0.
3x + 2 ≥ 0
Solve this linear inequality.
3x ≥ -2
2
x
3
The domain is all real numbers greater than or equal to -2/3. As long as the input value for x is greater
than or equal to -2/3, the function will produce a real number value.
2
2
Domain:
,
or
x
|
x
3
3
Example 3 :
What is the domain for
f
x
2
x
6
?
-2x + 6 ≥ 0
Since this is an even root, the radicand can not be
negative.
-2x ≥ -6
Divide both sides by -2. Remember to switch the
x ≤ 3
direction of the inequality.
V. Zabrocki 2011
page 2
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