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
Question
![**Problem Statement:**
Let \( f(x) = 7x + 3 \). Find \( f^{-1}(x) \).
**Solution:**
\[ f^{-1}(x) = \] [Enter your answer here in the space provided.]
---
**Explanation:**
To find the inverse of the function, \( f(x) = 7x + 3 \), follow these steps:
1. Replace \( f(x) \) with \( y \):
\[ y = 7x + 3 \]
2. Solve for \( x \) in terms of \( y \):
\[ y - 3 = 7x \]
\[ x = \frac{y - 3}{7} \]
3. Replace \( y \) with \( x \) to get the inverse function:
\[ f^{-1}(x) = \frac{x - 3}{7} \]
Therefore, the inverse function is \( f^{-1}(x) = \frac{x - 3}{7} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4e7be12-e868-44b9-86d4-0a000fb9596b%2F0bd29447-104c-47cf-9d3a-d9e119d6f62d%2Fq5c8tco_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Let \( f(x) = 7x + 3 \). Find \( f^{-1}(x) \).
**Solution:**
\[ f^{-1}(x) = \] [Enter your answer here in the space provided.]
---
**Explanation:**
To find the inverse of the function, \( f(x) = 7x + 3 \), follow these steps:
1. Replace \( f(x) \) with \( y \):
\[ y = 7x + 3 \]
2. Solve for \( x \) in terms of \( y \):
\[ y - 3 = 7x \]
\[ x = \frac{y - 3}{7} \]
3. Replace \( y \) with \( x \) to get the inverse function:
\[ f^{-1}(x) = \frac{x - 3}{7} \]
Therefore, the inverse function is \( f^{-1}(x) = \frac{x - 3}{7} \).
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