4 What is the inverse of F(x) = 4x-12? |a₁ y = ₁17-12 b.y = = (x+12) (₁y ==—=— (x+12) d.y= = 7 (x-12)
4 What is the inverse of F(x) = 4x-12? |a₁ y = ₁17-12 b.y = = (x+12) (₁y ==—=— (x+12) d.y= = 7 (x-12)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer #4
![**Question 4:** What is the inverse of \( f(x) = 4x - 12 \)?
**Answer Choices:**
- **a.** \( y = \frac{1}{4x-12} \)
- **b.** \( y = \frac{1}{4}(x + 12) \)
- **c.** \( y = \frac{1}{3}(x + 12) \)
- **d.** \( y = \frac{1}{4}(x - 12) \)
**Explanation:**
To find the inverse of the function \( f(x) = 4x - 12 \), follow these steps:
1. Replace \( f(x) \) with \( y \):
\[ y = 4x - 12 \]
2. Swap \( x \) and \( y \):
\[ x = 4y - 12 \]
3. Solve for \( y \):
\[ x + 12 = 4y \]
\[ y = \frac{x + 12}{4} \]
\[ y = \frac{1}{4}(x + 12) \]
Thus, the inverse function is \( y = \frac{1}{4}(x + 12) \). So, the correct answer is **b.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fce351b-90e5-44a7-899d-c11bfcc32a90%2Fa819a52b-021d-4810-8db0-5d015cbf6b06%2Fo09sco_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 4:** What is the inverse of \( f(x) = 4x - 12 \)?
**Answer Choices:**
- **a.** \( y = \frac{1}{4x-12} \)
- **b.** \( y = \frac{1}{4}(x + 12) \)
- **c.** \( y = \frac{1}{3}(x + 12) \)
- **d.** \( y = \frac{1}{4}(x - 12) \)
**Explanation:**
To find the inverse of the function \( f(x) = 4x - 12 \), follow these steps:
1. Replace \( f(x) \) with \( y \):
\[ y = 4x - 12 \]
2. Swap \( x \) and \( y \):
\[ x = 4y - 12 \]
3. Solve for \( y \):
\[ x + 12 = 4y \]
\[ y = \frac{x + 12}{4} \]
\[ y = \frac{1}{4}(x + 12) \]
Thus, the inverse function is \( y = \frac{1}{4}(x + 12) \). So, the correct answer is **b.**
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