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)}

Given:

Different functions in the ordered pairs.

To find:

The function which has an inverse that is also a  function.

Solution:

A relation is a function, if there exist unique output for each input.

The inverse of a function is a function, if there exist unique input for each output in the function.

It means, the inverse of a function is a function if each y value has unique x-value.

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

For y=4 we have x=0 and x=7, therefore, the inverse of this function is not a function.

In {(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} ,

For y=4 we have x=0 and x=5, therefore, the inverse of this function is not a function.

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

For all y value we have unique x values, therefore, the inverse of this function is a function.

In {(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)},

For y=4 we have x=-1 and x=0, therefore, the inverse of this function is not a function.

Therefore, the correct option is C.

answer: 177/8

step-by-step explanation: