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Finding the Domain of Algebraic Functions

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

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Summary: Finding the domain of various algebraic functions

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When finding domain consider the following:

  • In rational functions, the denominator cannot equal 0
  • When even-degreed roots are in the numerator, the expression under the radical must be greater than or equal to 0
  • When even-degreed roots are in the denominator, the expression under the radical must be greater than 0

Exercise 1

y=12−x y 12 x

Solution

-∞12 12 since 12−x≥0 12 x 0

Exercise 2

y=x2+9x−20 y x 2 9 x 20

Solution

-∞∞ since there are no even-degreed roots and it is not a rational function

Exercise 3

y=x2+6x+5 y x 2 6 x 5

Solution

-∞-5⋃-1∞ -5 -1 since x2+6x+5≥0 x 2 6 x 5 0

Exercise 4

y=x−2x+4 y x 2 x 4

Solution

-4∞ -4 since x+4>0 x 4 0

Exercise 5

y=7−xx y 7 x x

Solution

-∞0⋃07 0 0 7 since 7−x≥0 7 x 0 and x≠0 x 0

Exercise 6

y=x−1x2−4x y x 1 x 2 4 x

Solution

-∞0⋃4∞ 0 4 since x2−4x>0 x 2 4 x 0

Exercise 7

y=x2−1x2−4 y x 2 1 x 2 4

Solution

-∞-2⋃-2-1⋃12⋃2∞ -2 -2 -1 1 2 2 since x2−1≥0 x 2 1 0 and x2−4≠0 x 2 4 0

Exercise 8

y=3x−1x+5 y 3 x 1 x 5

Solution

025⋃25∞ 0 25 25 since x+5≠0 x 5 0 and x≥0 x 0

Exercise 9

1|x+1| 1 x 1

Solution

-1∞ -1 since x+1>0 x 1 0

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