NOV 2 Remaining "How Did I Do?" Uses: 1/3 Use function composition to determine if f (x) and g(x) are inverse functions. Yes, they are inverse functions. No, they are not inverse functions. Show your work and explain, in your own words, how you arrived at your answers. There are sample student explanations in the feedback to questions 3, 5, 9, and 14 that show the level of detail that is expected in your explanations. ΩΣ 61 Equation just need the explanation part body p span strong f(x) = 3x - 1 and g(x) = x³ + 1 L ( tv E A- T BIUS X, x² Paragraph Font C 22 Words: 6 A Submit Assignment 1 Quit & Save Aa B- ...
NOV 2 Remaining "How Did I Do?" Uses: 1/3 Use function composition to determine if f (x) and g(x) are inverse functions. Yes, they are inverse functions. No, they are not inverse functions. Show your work and explain, in your own words, how you arrived at your answers. There are sample student explanations in the feedback to questions 3, 5, 9, and 14 that show the level of detail that is expected in your explanations. ΩΣ 61 Equation just need the explanation part body p span strong f(x) = 3x - 1 and g(x) = x³ + 1 L ( tv E A- T BIUS X, x² Paragraph Font C 22 Words: 6 A Submit Assignment 1 Quit & Save Aa B- ...
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Determining Inverse Functions
**Task: Use function composition to determine if \( f(x) \) and \( g(x) \) are inverse functions.**
Given:
- \( f(x) = \sqrt[3]{x-1} \)
- \( g(x) = x^3 + 1 \)
**Choices:**
- [ ] Yes, they are inverse functions.
- [x] No, they are not inverse functions.
**Instructions:**
Explain your work and provide reasoning in your own words, detailing how you arrived at your answer. Here are sample student explanations like those for questions 3, 5, 9, and 14 to guide the level of detail expected in your explanation.
**Student Input Section:**
"I just need the explanation part."
---
For this problem, you need to show that either \( f(g(x)) = x \) and \( g(f(x)) = x \) are true, or provide evidence that they are not equal. Consider substituting one function into the other to check if they simplify to \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7e9c79f-8a95-4aea-89f2-f9a24ba7a1c3%2F329614fe-4c37-430e-a8aa-d45bca22992b%2Fo9hy9ek_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining Inverse Functions
**Task: Use function composition to determine if \( f(x) \) and \( g(x) \) are inverse functions.**
Given:
- \( f(x) = \sqrt[3]{x-1} \)
- \( g(x) = x^3 + 1 \)
**Choices:**
- [ ] Yes, they are inverse functions.
- [x] No, they are not inverse functions.
**Instructions:**
Explain your work and provide reasoning in your own words, detailing how you arrived at your answer. Here are sample student explanations like those for questions 3, 5, 9, and 14 to guide the level of detail expected in your explanation.
**Student Input Section:**
"I just need the explanation part."
---
For this problem, you need to show that either \( f(g(x)) = x \) and \( g(f(x)) = x \) are true, or provide evidence that they are not equal. Consider substituting one function into the other to check if they simplify to \( x \).
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