Question

Which function has an inverse that is also a function?

Answer 1

Answer:  The correct option is

(C) {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

Step-by-step explanation:  We are given to select the function having an inverse that is also a function.

We know that

a set of ordered pairs is a function if each first element is associated to one and only one second element.

The inverse of a function in the form of ordered pairs is formed by interchanging the first and second elements of each ordered pair.

Option (A) :

The given function is :

F = {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)}.

So, its inverse will be

F' = {(–2, -1), (4, 0), (3, 1), (14, 5), (4, 7)}.

Since the first element 4 is associated to two second elements 0 and 7.

So, the given function is not a function. Option (A) is incorrect.

Option (B) :

The given function is :

F = {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}.

So, its inverse will be

F' = {(2, -1), (4, 0), (5, 1), (4, 5), (2, 7)}.

Since the first element 2 is associated to two second elements -1 and 7.

So, the given function is not a function. Option (B) is incorrect.

Option (C) :

The given function is :

F = {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}.

So, its inverse will be

F' = {(3, -1), (4, 0), (14, 1), (6, 5), (2, 7)}.

Since each first element of the inverse is associated to one and only one second element, so the inverse F' is also a function.

Option (C) is CORRECT.

Option (D) :

The given function is :

F = {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}.

So, its inverse will be

F' = {(4, -1), (4, 0), (2, 1), (3, 5), (1, 7)}.

Since the first element 4 is associated to two second elements -1 and 0.

So, the given function is not a function. Option (D) is incorrect.

Thus, (C) is the correct option.

Answer 2

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