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Finding the Domain of Algebraic Functions

Module by: Pradnya Bhawalkar, Kim Johnston

Summary: 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
Problem 1
y=12-x y 12 x
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Solution 1
-12 12 since 12-x0 12 x 0
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Problem 2
y=x2+9x-20 y x 2 9 x 20
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Solution 2
- since there are no even-degreed roots and it is not a rational function
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Problem 3
y=x2+6x+5 y x 2 6 x 5
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Solution 3
--5-1 -5 -1 since x2+6x+50 x 2 6 x 5 0
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Problem 4
y=x-2x+4 y x 2 x 4
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Solution 4
-4 -4 since x+4>0 x 4 0
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Problem 5
y=7-xx y 7 x x
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Solution 5
-007 0 0 7 since 7-x0 7 x 0 and x0 x 0
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Problem 6
y=x-1x2-4x y x 1 x 2 4 x
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Solution 6
-04 0 4 since x2-4x>0 x 2 4 x 0
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Problem 7
y=x2-1x2-4 y x 2 1 x 2 4
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Solution 7
--2-2-1122 -2 -2 -1 1 2 2 since x2-10 x 2 1 0 and x2-40 x 2 4 0
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Problem 8
y=3x-1x+5 y 3 x 1 x 5
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Solution 8
02525 0 25 25 since x+50 x 5 0 and x0 x 0
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Problem 9
1|x+1| 1 x 1
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Solution 9
-1 -1 since x+1>0 x 1 0
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