Question

which function has an inverse that is also a function?
${(-1, -2), (0, 4), (1, 3), (5, 14), (7, 4)}$
${(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}$
${(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}$
${(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}$

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 maps to exactly one input, i.e., no repeated y-values).

Step2: Check set 1 y-values

Set 1: y-values are -2, 4, 3, 14, 4. Repeated y=4 → not one-to-one.

Step3: Check set 2 y-values

Set 2: y-values are 2, 4, 5, 4, 2. Repeated y=2 and y=4 → not one-to-one.

Step4: Check set 3 y-values

Set 3: y-values are 3, 4, 14, 6, 2. All unique → one-to-one.

Step5: Check set 4 y-values

Set 4: y-values are 4, 4, 2, 3, 1. Repeated y=4 → not one-to-one.

Answer:

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