Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Concept explainers
Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
Question
![The image contains a handwritten mathematical problem that is ideal for an educational website. Below is the transcription of the content along with a structural explanation:
---
### Problem Statement
**Objective:** Let \( f \) be a one-to-one function. Find the inverse function of the following:
#### a) \( F(x) = \frac{1 + 2x}{5} \)
---
### Explanation:
The task requires finding the inverse of the given function, \( F(x) = \frac{1 + 2x}{5} \). To find the inverse, follow these steps:
1. **Rewrite the function:** Start by expressing it in the form of \( y = F(x) \).
\[
y = \frac{1 + 2x}{5}
\]
2. **Swap \( y \) and \( x \):** This step prepares the equation to solve for \( y \) in terms of \( x \).
\[
x = \frac{1 + 2y}{5}
\]
3. **Solve for \( y \):** Isolate \( y \) on one side of the equation.
\[
5x = 1 + 2y \\
5x - 1 = 2y \\
y = \frac{5x - 1}{2}
\]
4. **Express the inverse function:** The inverse function, denoted as \( F^{-1}(x) \), is therefore
\[
F^{-1}(x) = \frac{5x - 1}{2}
\]
### Conclusion:
The inverse of the function \( F(x) = \frac{1 + 2x}{5} \) is
\[
F^{-1}(x) = \frac{5x - 1}{2}.
\]
---
This example is a good demonstration of how to derive the inverse of a linear function, a fundamental concept in algebra and calculus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2c5c293-7ff8-490b-b548-13e2f43ca7a8%2Fa9a87c1c-e050-49ea-afaf-ba062e113fba%2Fy3xvgg.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a handwritten mathematical problem that is ideal for an educational website. Below is the transcription of the content along with a structural explanation:
---
### Problem Statement
**Objective:** Let \( f \) be a one-to-one function. Find the inverse function of the following:
#### a) \( F(x) = \frac{1 + 2x}{5} \)
---
### Explanation:
The task requires finding the inverse of the given function, \( F(x) = \frac{1 + 2x}{5} \). To find the inverse, follow these steps:
1. **Rewrite the function:** Start by expressing it in the form of \( y = F(x) \).
\[
y = \frac{1 + 2x}{5}
\]
2. **Swap \( y \) and \( x \):** This step prepares the equation to solve for \( y \) in terms of \( x \).
\[
x = \frac{1 + 2y}{5}
\]
3. **Solve for \( y \):** Isolate \( y \) on one side of the equation.
\[
5x = 1 + 2y \\
5x - 1 = 2y \\
y = \frac{5x - 1}{2}
\]
4. **Express the inverse function:** The inverse function, denoted as \( F^{-1}(x) \), is therefore
\[
F^{-1}(x) = \frac{5x - 1}{2}
\]
### Conclusion:
The inverse of the function \( F(x) = \frac{1 + 2x}{5} \) is
\[
F^{-1}(x) = \frac{5x - 1}{2}.
\]
---
This example is a good demonstration of how to derive the inverse of a linear function, a fundamental concept in algebra and calculus.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education