Question

Which function has an inverse that is also a function? {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} {(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)} {(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)} {(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

Answer 1

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.

Answer 2

(-4,4) because its at the same hold for the other functions