which function has an inverse that is also a function?\n{(-1, -2), (0, 4), (1, 3), (5, 14), (7, 4)}\n{(-1…

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 set of ordered pairs

For the set ${(-1,-2),(0,4),(1,3),(5,14),(7,4)}$, the output value $4$ is associated with both $0$ and $7$, so it is not one - to - one. For the set ${(-1,2),(0,4),(1,5),(5,4),(7,2)}$, the output value $2$ is associated with $- 1$ and $7$, and the output value $4$ is associated with $0$ and $5$, so it is not one - to - one. For the set ${(-1,3),(0,4),(1,14),(5,6),(7,2)}$, each output value is associated with a unique input value. So this function is one - to - one. For the set ${(-1,4),(0,4),(1,2),(5,3),(7,1)}$, the output value $4$ is associated with $-1$ and $0$, so it is not one - to - one.

Answer:

${(-1,3),(0,4),(1,14),(5,6),(7,2)}$