Question

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

Explanation:

Step1: Recall inverse function rule

A function has an inverse that is also a function if and only if the original function is one-to-one (each output corresponds to exactly one input, no repeated y-values).

Step2: Check Option 1 y-values

Y-values: $3, 7, 0, -3, -7$. All are unique.

Step3: Check Option 2 y-values

Y-values: $6, 2, 6, 2, 2$. Repeated values exist.

Step4: Check Option 3 y-values

Y-values: $5, 9, 8, 8, 4$. Repeated values exist.

Step5: Check Option 4 y-values

Y-values: $4, -1, 0, 1, 1$. Repeated values exist.

Answer:

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