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 function problems, ideal for students preparing for AP exams. It includes step-by-step answers for various functions, covering domains and ranges, and offers practice problems with solutions. This resource is essential for understanding the concepts of inverse functions, making it suitable for AP Precalculus students. The answer key aligns with the curriculum and helps reinforce learning through practice and application.

Key Points

  • Includes solutions for inverse functions problems in AP Precalculus.
  • Covers domains and ranges for various functions, enhancing understanding.
  • Provides practice problems with detailed answers for effective learning.
  • Essential resource for AP students preparing for exams on inverse functions.
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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 various types of functions such as quadratic, square root, and rational functions. Each function is analyzed to find its inverse, and the domain and range are discussed in detail. This comprehensive approach helps students understand how to derive inverses for different function types, which is crucial for mastering the topic.
How does the answer key assist with understanding inverse functions?
The answer key provides step-by-step solutions that clarify the process of finding inverse functions. By breaking down each problem, students can follow the logic and methodology used to arrive at the answers. This not only aids in solving similar problems but also reinforces the underlying concepts of inverse functions, making it a valuable study tool.
What is the significance of domain and range in inverse functions?
Understanding the domain and range is critical when working with inverse functions, as they determine the valid inputs and outputs of the function. The answer key emphasizes these aspects by providing specific details for each function analyzed. This focus helps students grasp how the domain and range of a function relate to its inverse, which is a key concept in precalculus.
Are there practice problems included in the answer key?
Yes, the answer key includes practice problems that allow students to apply what they have learned about inverse functions. These problems are designed to reinforce the concepts covered in the section and provide opportunities for independent practice. Solutions are provided for each problem, making it easier for students to check their work and understand any mistakes.
How can students use this answer key effectively for exam preparation?
Students can use the answer key as a study guide by first attempting the problems on their own before checking their answers. This approach promotes active learning and helps identify areas where they may need further review. Additionally, the detailed explanations in the answer key provide insights into the reasoning behind each solution, which is beneficial for mastering the topic ahead of exams.