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

Explanation:

Step1: Recall the condition for inverse to be a function

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

Step2: Check each option

For the set ${(-4,3),(-2,7),(-1,0),(4, - 3),(11,-7)}$: The output values $3,7,0,-3,-7$ are all distinct for the input values $-4,-2,-1,4,11$ respectively. For the set ${(-4,6),(-2,2),(-1,6),(4,2),(11,2)}$: The output value $6$ corresponds to $-4$ and $-1$, and the output value $2$ corresponds to $-2$, $4$ and $11$, so it is not one - to - one. For the set ${(-4,5),(-2,9),(-1,8),(4,8),(11,4)}$: The output value $8$ corresponds to $-1$ and $4$, so it is not one - to - one. For the set ${(-4,4),(-2,-1),(-1,0),(4,1),(11,1)}$: The output value $1$ corresponds to $4$ and $11$, so it is not one - to - one.

Answer:

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