Finding the Domain of Algebraic Functions
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
Solution 1
- ∞ 12
12
12 - x ≥ 0 12
x
0
Problem 2
y = x 2 + 9 x - 20 y
x
2
9
x
20
Solution 2
- ∞ ∞
Problem 3
y = x 2 + 6 x + 5 y
x
2
6
x
5
Solution 3
- ∞ -5 ⋃ -1 ∞
-5
-1
x 2 + 6 x + 5 ≥ 0 x
2
6
x
5
0
Problem 4
y = x - 2 x + 4 y
x
2
x
4
Solution 4
-4 ∞
-4
x + 4 > 0 x
4
0
Problem 5
y = 7 - x x y
7
x
x
Solution 5
- ∞ 0 ⋃ 0 7
0
0
7
7 - x ≥ 0 7
x
0
x ≠ 0 x
0
Problem 6
y = x - 1 x 2 - 4 x y
x
1
x
2
4
x
Solution 6
- ∞ 0 ⋃ 4 ∞
0
4
x 2 - 4 x > 0 x
2
4
x
0
Problem 7
y = x 2 - 1 x 2 - 4 y
x
2
1
x
2
4
Solution 7
- ∞ -2 ⋃ -2 -1 ⋃ 1 2 ⋃ 2 ∞
-2
-2
-1
1
2
2
x 2 - 1 ≥ 0 x
2
1
0
x 2 - 4 ≠ 0 x
2
4
0
Problem 8
y = 3 x - 1 x + 5 y
3
x
1
x
5
Solution 8
0 25 ⋃ 25 ∞
0
25
25
x + 5 ≠ 0 x
5
0
x ≥ 0 x
0
Problem 9
1 | x + 1 | 1
x
1
Solution 9
-1 ∞
-1
x + 1 > 0 x
1
0
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This work is licensed by Pradnya Bhawalkar and Kim Johnston. See the Creative Commons License about permission to reuse this material.
Last edited by Pradnya Bhawalkar on May 2, 2006 10:39 pm GMT-5.