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Finding the Domain of Radical Functions

Module by: Pradnya Bhawalkar, Kim Johnston. E-mail the authors

Summary: Finding the domain of radical/root functions.

When finding 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 y x

x x≥0 x x 0

PRACTICE - Find the Domain of the following:

Exercise 1

y=2⁢x−5 y 2x5

[ Show Solution ]

Exercise 2

y=7−x4 y 4 7x

[ Show Solution ]

The rest of the answers will be expressed in interval notation since that is a simpler way to express answers.

Exercise 3

y=4⁢x2−164 y 4 4x216

[ Show Solution ]

Exercise 4

y=16−25⁢x2 y 16 25 x 2

[ Show Solution ]

Exercise 5

y=(x−7)⁢(x+1) y x 7 x 1

[ Show Solution ]

Exercise 6

y=2⁢x2−7⁢x+3 y 2 x 2 7 x 3

[ Show Solution ]

Exercise 7

y=x⁢x2+4 y x x 2 4

[ Show Solution ]

Exercise 8

y=x+−x+8 y x x8

[ Show Solution ]

Exercise 9

y=6⁢x2+8 y 6x28

[ Show Solution ]

Exercise 10

y=(−8)−6⁢x2 y 86x2

[ Show Solution ]

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