To determine which function has an inverse that is also a function, we need to look at the given sets of points and see if the y-values (ranges) are unique. If the y-values are unique, then the function has an inverse that is also a function.
Given the sets of points:
1. [tex]\(\{(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)\}\)[/tex]
2. [tex]\(\{(-4, 6), (-2, 2), (-1, 6), (4, 2), (11, 2)\}\)[/tex]
3. [tex]\(\{(-4, 5), (-2, 9), (-1, 8), (4, 8), (11, 4)\}\)[/tex]
4. [tex]\(\{(-4, 4), (-2, -1), (-1, 0), (4, 1), (11, 1)\}\)[/tex]
We need to check each set to see if it contains any duplicate y-values (outputs).
### Set 1: [tex]\(\{(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)\}\)[/tex]
- Corresponding y-values: [tex]\(\{3, 7, 0, -3, -7\}\)[/tex]
- All y-values are unique.
### Set 2: [tex]\(\{(-4, 6), (-2, 2), (-1, 6), (4, 2), (11, 2)\}\)[/tex]
- Corresponding y-values: [tex]\(\{6, 2, 6, 2, 2\}\)[/tex]
- Duplicate y-values: 6 and 2.
### Set 3: [tex]\(\{(-4, 5), (-2, 9), (-1, 8), (4, 8), (11, 4)\}\)[/tex]
- Corresponding y-values: [tex]\(\{5, 9, 8, 8, 4\}\)[/tex]
- Duplicate y-values: 8.
### Set 4: [tex]\(\{(-4, 4), (-2, -1), (-1, 0), (4, 1), (11, 1)\}\)[/tex]
- Corresponding y-values: [tex]\(\{4, -1, 0, 1, 1\}\)[/tex]
- Duplicate y-values: 1.
### Conclusion:
The only set with all unique y-values is Set 1: [tex]\(\{(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)\}\)[/tex]. This means its inverse, if it exists, is also a function.
Thus, the function with the given points [tex]\(\{(-4,3),(-2,7),(-1,0),(4,-3),(11,-7)\}\)[/tex] has an inverse that is also a function. This is Set 1.
