OpenStax-CNX module: m13583
1
Finding the Domain of Radical
Functions
∗
Pradnya Bhawalkar
Kim Johnston
This work is produced by OpenStax-CNX and licensed under the
†
Creative Commons Attribution License 2.0
Abstract
Finding the domain of radical/root functions.
When nding the domain of even-degree roots, the expression under the radical must be greater than or
equal to 0.
Example 1
Find the domain of y =
√
x
{x | x ≥ 0}
PRACTICE - Find the Domain of the following:
Exercise
1
√
(Solution on p. 3.)
Exercise
√ 2
(Solution on p. 3.)
2x − 5
y=
y=
4
7−x
The rest of the answers will be expressed in interval notation since that is a simpler way to express answers.
Exercise
√ 3
(Solution on p. 3.)
Exercise
4
√
(Solution on p. 3.)
Exercise
p 5
(Solution on p. 3.)
Exercise
6
√
(Solution on p. 3.)
y=
4
4x2 − 16
16 − 25x2
y=
(x − 7) (x + 1)
y=
2x2 − 7x + 3
y=
Exercise
√7
y=x
x2 + 4
(Solution on p. 3.)
Exercise√8
y =x+
∗ Version
−x + 8
1.3: Apr 27, 2006 3:34 pm -0500
† http://creativecommons.org/licenses/by/2.0/
http://cnx.org/content/m13583/1.3/
(Solution on p. 3.)
OpenStax-CNX module: m13583
2
Exercise
9
√
(Solution on p. 3.)
Exercise
p 10
(Solution on p. 3.)
y=
y=
6x2 + 8
(−8) − 6x2
http://cnx.org/content/m13583/1.3/
OpenStax-CNX module: m13583
3
Solutions to Exercises in this Module
Solution
to Exercise (p. 1)
x|x≥
5
2
since 2x − 5 ≥ 0, 2x ≥ 5, x ≥
Solution to Exercise (p. 1)
5
2
{ x | x ≤ 7 } since 7 − x ≥ 0, −x ≥ −7, x ≤ 7
Solution to Exercise (p. 1)
(−∞, −2] ∪ [2, ∞) since 4x2 − 16 ≥ 0, 4x2 ≥ 16, x2 ≥ 4, (x ≤ −2) ∨ (x ≥ 2)
Solution
to Exercise (p. 1)
−4 4
5 , 5
since 16 − 25x2 ≥ 0, −25x2 ≥ −16, x2 ≤
Solution to Exercise
p (p. 1)
(−∞, −1] ∪ [7, ∞),
16
25 ,
x≥
−4
5
∧
x≤
4
5
(x − 7) (x + 1) ≥ 0
Solution to Exercise (p. 1)
(−∞, 1/2] ∪ [3, ∞), 2x2 − 7x + 3 ≥ 0, (2x − 1) (x − 3) ≥ 0, x ≤
Solution to Exercise (p. 1)
1
2
∨ (x ≥ 3)
(−∞, ∞), since x2 + 4 ≥ 0, x2 ≥ −4 This will always be true, for all real numbers, any number squared is
always positive
Solution to Exercise (p. 1)
(−∞, 8] since −x + 8 ≥ 0, −x ≥ −8, x ≤ 8
Solution to Exercise (p. 1)
(−∞, ∞), since 6x2 + 8 ≥ 0, 6x2 ≥ −8, x2 ≥
squared is always positive
Solution to Exercise (p. 2)
−8
6
This will always be true, for all real numbers, any number
No solution since (−8) − 6x2 ≥ 0, −6x2 ≥ 8, x2 ≥ −8
6 This will never be true, so there is no solution, since
any number squared is always positive, so it will never be less than 0.
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