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.