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,...
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Question
![**Problem Statement:**
Find an equation of the inverse relation.
\[ x = y^2 - 3y \]
**Explanation:**
To find the inverse relation of the given equation, you will need to express \( y \) in terms of \( x \), and then swap the variables. Here’s how to do it:
1. Start with the original equation:
\[ x = y^2 - 3y \]
2. Solve for \( y \) using algebraic manipulation. This will involve solving a quadratic equation in terms of \( y \).
3. Once you find \( y \), switch \( x \) and \( y \) to express the inverse relation.
There are no graphs or diagrams associated with this problem, as it is purely algebraic. However, understanding the solution might involve visualizing the function and its inverse on a coordinate plane. Keep in mind that not all functions have inverses that are functions themselves, especially if the original equation is not one-to-one.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1b7a372-1344-4f7f-af15-7d7e9d0720e7%2F4b59f16b-d7a8-457e-932a-4ba7729c8234%2Fybromr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find an equation of the inverse relation.
\[ x = y^2 - 3y \]
**Explanation:**
To find the inverse relation of the given equation, you will need to express \( y \) in terms of \( x \), and then swap the variables. Here’s how to do it:
1. Start with the original equation:
\[ x = y^2 - 3y \]
2. Solve for \( y \) using algebraic manipulation. This will involve solving a quadratic equation in terms of \( y \).
3. Once you find \( y \), switch \( x \) and \( y \) to express the inverse relation.
There are no graphs or diagrams associated with this problem, as it is purely algebraic. However, understanding the solution might involve visualizing the function and its inverse on a coordinate plane. Keep in mind that not all functions have inverses that are functions themselves, especially if the original equation is not one-to-one.
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