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Finding the domain of various algebraic functions

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

y 12 x

12 since 12 x 0

y x 2 9 x 20

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

y x 2 6 x 5

-5 -1 since x 2 6 x 5 0

y x 2 x 4

-4 since x 4 0

y 7 x x

0 0 7 since 7 x 0 and x 0

y x 1 x 2 4 x

0 4 since x 2 4 x 0

y x 2 1 x 2 4

-2 -2 -1 1 2 2 since x 2 1 0 and x 2 4 0

y 3 x 1 x 5

0 25 25 since x 5 0 and x 0

1 x 1

-1 since x 1 0

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Source:  OpenStax, "rational"ity. OpenStax CNX. May 03, 2006 Download for free at http://cnx.org/content/col10350/1.2
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