Question

Which function has an inverse that is also a function?
A. {(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)}
B. {(-4, 6), (-2, 2), 6-1, 6), (4, 2), (11, 2)}
C. {(-4,5), (-2, 9), (–1, 8), (4, 8), (11,4)}
D. {(-4, 4), (-2, -1), (–1, 0). (4.1), (11, 1)}

Answer 1

Given:

The different functions in the form of set of ordered pairs.

To find:

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

Solution:

A relation is a function if there exists unique y-value for each x-value.

We know that the inverse transformation is defined as:

$(x,y)\to (y,x)$

So, the inverse of function is also a function if their exists unique x-value for each y-value in the function.

In option A, all x-values and y-values are unique. It means, inverse of this function is also a function. So, option A is correct.

In option B, $x=-4$ and $x=-1$ when $y=6$. It means, inverse of this function is not a function. So, option B is incorrect.

In option C, $x=-1$ and $x=4$ when $y=8$. It means, inverse of this function is not a function. So, option C is incorrect.

In option D, $x=4$ and $x=11$ when $y=1$. It means, inverse of this function is not a function. So, option D is incorrect.

Therefore, the correct option is A.