Answer: The correct option is
(A) {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}.
Step-by-step explanation: We are given to select the function having an inverse that is also a function.
We know that
a Relation as a set of ordered pairs is a function if each x co-ordinate does not correspond to two different y co-ordinates.
Option (A) : F = {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}.
Here, the inverse of F will be
R = {(3, -4), (-2, 7), (0, -1), (-3, 4), (-7, 11)}.
Since no x co-ordinate corresponds to more than one y co-ordinate, so this inverse will be a function.
Option (A) is CORRECT.
Option (B) : F = {(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)}.
Here, the inverse of F will be
R = {(6, -4), (2, -2), (6, -1), (2, 4), (2, 11)}.
Since the x co-ordinate corresponds to three different y co-ordinates (-2, 4 and 11), so this inverse will NOT be a function.
Option (B) is not correct
Option (C) : F = {(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)}.
Here, the inverse of F will be
R = {(5, -4), (9, -2), (8, -1), (8, 4), (4, 11)}.
Since the x co-ordinate 8 corresponds to two different y co-ordinates (-1 and 4), so this inverse will NOT be a function.
Option (C) is not correct.
Option (D) : F = {(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}.
Here, the inverse of F will be
R = {(4, -4), (-1, -2), (0, -1), (1, 4), (1, 11)}.
Since the x co-ordinate 1 corresponds to two different y co-ordinates (4 and 11), so this inverse will NOT be a function.
Option (D) is not correct.
Thus, (A) is the correct option.
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