which function has an inverse that is also a function?\no {(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)}\no…

Answer:

A. ${(-4,3),(-2,7),(-1,0),(4, - 3),(11,-7)}$

Explanation:

Step1: Recall inverse - function condition

A function has an inverse that is also a function if and only if it is one - to - one. A one - to - one function has no two different input values that produce the same output value.

Step2: Check option A

In the set ${(-4,3),(-2,7),(-1,0),(4, - 3),(11,-7)}$, each $y$ - value is unique for different $x$ - values.

Step3: Check option B

In the set ${(-4,6),(-2,2),(-1,6),(4,2),(11,2)}$, the $y$ - value $6$ corresponds to $x=-4$ and $x = - 1$, and the $y$ - value $2$ corresponds to $x=-2$, $x = 4$ and $x = 11$. It is not one - to - one.

Step4: Check option C

In the set ${(-4,5),(-2,9),(-1,8),(4,8),(11,4)}$, the $y$ - value $8$ corresponds to $x=-1$ and $x = 4$. It is not one - to - one.

Step5: Check option D

In the set ${(-4,4),(-2,-1),(-1,0),(4,1),(11,1)}$, the $y$ - value $1$ corresponds to $x = 4$ and $x = 11$. It is not one - to - one.