AP Precalculus 2.8 Inverse Functions Answer Key

AP Precalculus 2.8 Inverse Functions Answer Key

The AP Precalculus 2.8 Inverse Functions Answer Key provides detailed solutions for inverse functions, essential for students preparing for AP exams. It covers various types of functions, including quadratic, square root, and rational functions, with step-by-step explanations. This resource is designed for high school students mastering inverse functions concepts and their applications. The answer key includes domain and range specifications, making it a comprehensive tool for understanding the topic.

Key Points

  • Includes solutions for inverse functions in AP Precalculus.
  • Covers quadratic, square root, and rational functions.
  • Provides domain and range for each inverse function.
  • Designed for high school students preparing for AP exams.
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© The Algebros from FlippedMath.com
2.8 Inverse Functions
AP Precalculus
Find the inverse of each function and list the domain and range of
𝒇
𝟏
󰇛
𝒙
󰇜
.
1.
𝑓
󰇛
𝑥
󰇜
󰇛𝑥3󰇜
4
Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
2.
𝑓
󰇛
𝑥
󰇜
𝑥6
Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
3.
𝑓
󰇛
𝑥
󰇜
󰇛
𝑥1
󰇜
2 for 𝑥1
Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
4.
𝑓
󰇛
𝑥
󰇜
√
𝑥2 3
Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
5.
𝑓
󰇛
𝑥
󰇜
󰇛𝑥2󰇜
5 for 𝑥2
Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
6.
𝑓
󰇛
𝑥
󰇜

Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
7.
𝑓
󰇛
𝑥
󰇜

󰇛
𝑥4
󰇜
1 for 𝑥4
Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
8.
𝑓
󰇛
𝑥
󰇜

√
𝑥1 3
Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
9.
𝑓
󰇛
𝑥
󰇜
2𝑥5
3𝑥4
Domain of 𝑓

󰇛
𝑥
󰇜
:
Range of 𝑓

󰇛
𝑥
󰇜
:
2.8 Practice
© The Algebros from FlippedMath.com
Use the tables below to find the given values.
10.
𝒙
𝒇
󰇛
𝒙
󰇜
1 2
2 3
3 6
4 2
5 4
6 1
11.
𝒙
𝒇
󰇛
𝒙
󰇜
3 2
1 7
2 10
7 3
8 1
10 8
12.
𝒙
𝒇
󰇛
𝒙
󰇜
10 6
6 7
2 10
3 11
7 3
11 2
a.
𝑓
󰇛
1
󰇜
b. 𝑓
󰇛
6
󰇜
c.
𝑓

󰇛
1
󰇜
d.
𝑓

󰇛
4
󰇜
e. 𝑓
󰇛
2
󰇜
f.
𝑓

󰇛
6
󰇜
a.
𝑓
󰇛
2
󰇜
b. 𝑓
󰇛
10
󰇜
c.
𝑓

󰇛
7
󰇜
d.
𝑓

󰇛
3
󰇜
e. 𝑓
󰇛
7
󰇜
f.
𝑓

󰇛
2
󰇜
a.
𝑓
󰇛
10
󰇜
b. 𝑓
󰇛
3
󰇜
c.
𝑓

󰇛
7
󰇜
d.
𝑓

󰇛
6
󰇜
e. 𝑓
󰇛
7
󰇜
f.
𝑓

󰇛
2
󰇜
The graph of a function is given below. Identify if the function is invertible. Sketch the graph of the inverse
regardless of whether or not it is invertible.
13.
Is 𝑓
󰇛
𝑥
󰇜
invertible?
14.
Is 𝑔
󰇛
𝑥
󰇜
invertible?
15.
Is ℎ
󰇛
𝑥
󰇜
invertible?
Determine if the two functions are inverses of each other using composition.
16.
𝑓
󰇛
𝑥
󰇜
3𝑥5 and 𝑔
󰇛
𝑥
󰇜
𝑥
17.
𝑓
󰇛
𝑥
󰇜
√
3 𝑥
and 𝑔
󰇛
𝑥
󰇜
𝑥
3
𝑔󰇛𝑥󰇜
ℎ󰇛𝑥󰇜
𝑓
󰇛𝑥󰇜
© The Algebros from FlippedMath.com
18. The graph of the piecewise-linear function 𝑓 is shown in the figure. Let 𝑔
be the inverse function of 𝑓. What is the minimum value of 𝑔?
(A) 4
(B) 3
(C) 2
(D) 3
19. Mr. Brust is filling up his backdoor kiddie pool with the water hose. The amount of water, in gallons, in the pool 𝑡
minutes after he turns on the water can be modeled by 𝑃, an increasing function of time 𝑡. Which of the following
gives a verbal representation of the function 𝑃

, the inverse of 𝑃?
(A) 𝑃

is an increasing function of the amount of time after the water is turned on.
(B) 𝑃

is a decreasing function of the amount of time after the water is turned on.
(C) 𝑃

is an increasing function of the amount of water in the pool.
(D) 𝑃

is a decreasing function of the amount of water in the pool.
20.
𝑥 1 2 3 4 5
𝑓
󰇛
𝑥
󰇜
18 10 3 1 26
Calculator active. Let 𝑓 be an increasing function for 𝑥0. The table gives values of 𝑓
󰇛
𝑥
󰇜
at selected values of 𝑥. The
function 𝑔 is given by 𝑔
󰇛
𝑥
󰇜



a. The function ℎ is defined by ℎ
󰇛
𝑥
󰇜
󰇛
𝑔∘𝑓
󰇜󰇛
𝑥
󰇜
𝑔𝑓
󰇛
𝑥
󰇜
. Find the value of ℎ
󰇛
2
󰇜
as a decimal approximation or
indicate that it is not defined.
b. Find the value of 𝑓

󰇛
1
󰇜
, or indicate that it is not defined.
2.8 Test Prep
2.8 Inverse Functions
Graph of
𝑓
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End of Document
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FAQs of AP Precalculus 2.8 Inverse Functions Answer Key

What types of functions are covered in the inverse functions section?
The inverse functions section includes a variety of functions such as quadratic functions, square root functions, and rational functions. Each type is explored with specific examples that demonstrate how to find their inverses. The document also addresses the domain and range of these functions, providing a thorough understanding of their behavior. This comprehensive approach helps students grasp the fundamental concepts necessary for mastering inverse functions.
How does the answer key assist students in understanding inverse functions?
The answer key assists students by providing clear, step-by-step solutions to problems related to inverse functions. Each solution is accompanied by explanations that clarify the reasoning behind each step, making it easier for students to follow along. Additionally, the inclusion of domain and range for each function enhances their understanding of how inverses operate within specific constraints. This resource is invaluable for students preparing for AP exams, as it reinforces key concepts and problem-solving techniques.
What is the significance of domain and range in inverse functions?
Domain and range are crucial in understanding inverse functions because they define the set of possible input and output values. For an inverse function to exist, the original function must be one-to-one, meaning that each output corresponds to exactly one input. The answer key emphasizes the importance of determining the domain and range of both the original and inverse functions, which helps students visualize and comprehend the relationship between them. This understanding is essential for solving problems accurately in AP Precalculus.
Are there practice problems included in the inverse functions section?
Yes, the inverse functions section includes practice problems that allow students to apply the concepts they have learned. These problems vary in difficulty and cover different types of functions, providing a comprehensive review of the material. The answer key not only gives the solutions but also explains the methods used to arrive at those solutions, reinforcing learning. This practice is particularly beneficial for students preparing for the AP exam, as it helps them build confidence in their problem-solving skills.

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