Identify the graph of the inverse function of f, if it exists. -8-6-4 NAS 00 8 6 y 4- 12. -24 -4 -6 -8- 2 4 6 8 X
Identify the graph of the inverse function of f, if it exists. -8-6-4 NAS 00 8 6 y 4- 12. -24 -4 -6 -8- 2 4 6 8 X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
- Description: The red line in this graph has a negative slope. It intersects the y-axis at \( y = 2 \) and the x-axis at \( x = 2 \).
2. 
- Description: The red line in this graph has a negative slope. It intersects the y-axis at \( y = 2 \) and the x-axis at \( x = 2 \).
3. 
- Description: The red line in this graph has a positive slope. It intersects the y-axis at \( y = -2 \) and the x-axis at \( x = 2 \).
4.
- Description: The last option states, "The graph is a function that does not have an inverse function."
### Explanation:
To determine the inverse function graph, we need to assess whether the original function \( f \) is one-to-one (bijective). A function has an inverse if and only if it is one-to-one, meaning that every y-value has a unique corresponding x-value, and vice versa.
Given the presented options, analyze each graph's slope and intercepts, comparing them with the original function \( f \).
### Conclusion:
Select the appropriate graph or statement that correctly represents the inverse function of \( f \).
**Note:** Ensure to verify the one-to-one nature of the original function \( f \) through visual inspection or mathematical analysis before concluding.
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This content would be suitable for an educational website, guiding students through identifying inverse function graphs visually and analytically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd31fdfb-4046-4b08-9c18-d73722d2496d%2F8a5083e2-da63-458a-8514-627c69518a5b%2Fq3sad4o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Inverse Function Graph Identification Exercise**
---
**Identify the graph of the inverse function of \( f \), if it exists.**
---
### Problem Statement:
Examine the given graph of the function \( f \) and determine which graph among the options provided represents the inverse function of \( f \), provided it exists.
### Original Function Graph:
The graph of the function \( f \) is shown as a red line with a negative slope intersecting both the x-axis and y-axis at certain points. The line crosses the y-axis at approximately \( y = 2 \) and the x-axis at approximately \( x = 2 \).
### Multiple Choice Options:
1. 
- Description: The red line in this graph has a negative slope. It intersects the y-axis at \( y = 2 \) and the x-axis at \( x = 2 \).
2. 
- Description: The red line in this graph has a negative slope. It intersects the y-axis at \( y = 2 \) and the x-axis at \( x = 2 \).
3. 
- Description: The red line in this graph has a positive slope. It intersects the y-axis at \( y = -2 \) and the x-axis at \( x = 2 \).
4.
- Description: The last option states, "The graph is a function that does not have an inverse function."
### Explanation:
To determine the inverse function graph, we need to assess whether the original function \( f \) is one-to-one (bijective). A function has an inverse if and only if it is one-to-one, meaning that every y-value has a unique corresponding x-value, and vice versa.
Given the presented options, analyze each graph's slope and intercepts, comparing them with the original function \( f \).
### Conclusion:
Select the appropriate graph or statement that correctly represents the inverse function of \( f \).
**Note:** Ensure to verify the one-to-one nature of the original function \( f \) through visual inspection or mathematical analysis before concluding.
---
This content would be suitable for an educational website, guiding students through identifying inverse function graphs visually and analytically.
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