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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![### Understanding Inverse Functions
To begin, let us consider the function:
\[ f(x) = \frac{x + 4}{x + 6} \]
Our goal is to find the inverse function \( f^{-1}(x) \) for a given input.
#### Example Problem
Find \( f^{-1}(-10) \).
1. **Set up the equation for the inverse:**
\[ -10 = \frac{x + 4}{x + 6} \]
2. **Solve for the unknown variable:**
\[ -10(x + 6) = x + 4 \]
\[ -10x - 60 = x + 4 \]
\[ -11x = 64 \]
\[ x = -\frac{64}{11} \]
3. **Substitute the value back:**
\[ f^{-1}(-10) = -\frac{64}{11} \]
#### Conclusion
So, \( f^{-1}(-10) = -\frac{64}{11} \).
For further assistance, you can refer to the provided video help.
***Question Help:*** [Video Icon]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f8a397f-4115-4363-8e32-37a2c2950f08%2F7a25425c-1494-4811-b755-2344383b3442%2Fuh6xit_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Inverse Functions
To begin, let us consider the function:
\[ f(x) = \frac{x + 4}{x + 6} \]
Our goal is to find the inverse function \( f^{-1}(x) \) for a given input.
#### Example Problem
Find \( f^{-1}(-10) \).
1. **Set up the equation for the inverse:**
\[ -10 = \frac{x + 4}{x + 6} \]
2. **Solve for the unknown variable:**
\[ -10(x + 6) = x + 4 \]
\[ -10x - 60 = x + 4 \]
\[ -11x = 64 \]
\[ x = -\frac{64}{11} \]
3. **Substitute the value back:**
\[ f^{-1}(-10) = -\frac{64}{11} \]
#### Conclusion
So, \( f^{-1}(-10) = -\frac{64}{11} \).
For further assistance, you can refer to the provided video help.
***Question Help:*** [Video Icon]
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