Question

Which function has an inverse that is also a function? {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} {(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)} {(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)} {(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

Answer 1

{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}

Explanation:

If the function has an inverse that is also a function, there can only be one y for every x.

Choice A is correct because for every x value, there is only one y value.

Answer 2

• 1. {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}

Explanation:

• Info to consider:
• Inverse of a function: (x, y) → (y, x)
• Definition of a function: Every input will have exactly one output.

Let's analyze the functions:

1. {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}

• It has unique y- values, its inverse won't have repeat x-values, so the inverse is also a function

2. {(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)}

• It has repeat y values of 6 and 2. Its inverse it is going to cause repeat input numbers with different output. This won't be a function

3. {(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)}

• It has repeat y values of 8. Its inverse it is going to cause repeat input numbers with different output. This won't be a function

4. {(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

• It has repeat y values of 1. Its inverse it is going to cause repeat input numbers with different output. This won't be a function

So the first set of data is the only correct one