Function Inverses

Question 1

Identify the inverse g(x) of the given relation f(x).f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}

Revolt · Accepted Answer

g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}

Question 2

Choose a true statement.

Revolt · Accepted Answer

g(x) is a function because f(x) is one-to-one.

Question 3

a = ⇒ -3.8 b = ⇒ -2.6 c = ⇒ 1.7 d = ⇒ 4.4 e = ⇒ 1

Revolt · Accepted Answer

⇒ -3.8: -1; ⇒ -2.6: 0; ⇒ 1.7: 3; ⇒ 4.4: -1; ⇒ 1: 2

Question 4

Talib is trying to find the inverse of the function to the right. His work appears beneath it. Is his work correct? Explain your answer.

Revolt · Accepted Answer

No. His rearrangement is correct, but he must switch x and y to write the inverse: f⁻¹(x) = (x - 4)/-8 = (4 - x)/8.

Question 5

Select each graph that shows a function and its inverse.

Revolt · Accepted Answer

mr001-1.jpg; mr001-4.jpg

Question 6

If the graph of an inverse passes the , you know that the inverse is a function.

Revolt · Accepted Answer

vertical-line test

Question 7

The graph of an inverse is the reflection of the graph of the function over the line .

Revolt · Accepted Answer

y = x

Question 8

The composition of a function and its inverse is always .

Revolt · Accepted Answer

x

Question 9

The range values of an inverse are the values of the original function.

Revolt · Accepted Answer

domain

Question 10

f(x) = 4x − 12 f−1(x) = x +

Revolt · Accepted Answer

Part 1: 1/4; Part 2: 3

Function Inverses Answers