Function Operations

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

The composition of a function and its inverse is always .

Revolt · Accepted Answer

x

Question 4

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

Revolt · Accepted Answer

domain

Question 5

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

Revolt · Accepted Answer

origin

Question 6

f(x) = 4x − 12 f−1(x) = x +

Revolt · Accepted Answer

Part 1: 1/4; Part 2: 3

Question 7

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 8

Danika concludes that the following functions are inverses of each other because f(g(x)) = x. Do you agree with Danika? Explain your reasoning.f(x) = |x|g(x) = –x

Revolt · Accepted Answer

She is not correct. She forgot to do g compose f. To verify that functions are inverses of each other, you must also show that g(f(x)) x. Because g(f(x)) x, the functions are not inverses of each other. Compare your response to the sample response above.

Question 9

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

Revolt · Accepted Answer

x = 0

Question 10

Compare your response to the sample response above. What did you include in your explanation?

Revolt · Accepted Answer

that Danika needs to find g compose f; that g(f(x)) must also equal x; that g(f(x)) = –x

Function Operations Answers

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