Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.7: A Library Of Parent Functions
Problem 47E
Related questions
Question
![Certainly! Here’s the transcription suitable for an educational website:
---
### Problem Statement
**Given Function:**
\[ f(x) = (x + 4)^2 \]
#### Problem 1:
**Find a domain on which \( f \) is one-to-one and non-decreasing.**
\[ \boxed{\quad \quad \quad \quad \quad \quad} \]
#### Problem 2:
**Find the inverse of \( f \) restricted to this domain.**
\[ f^{-1}(x) = \boxed{\quad \quad \quad \quad} \]
---
Note: Since this problem involves both the properties of functions and the concept of inverse functions, a good grasp of these topics is beneficial.
- **One-to-one Function:** A function is one-to-one if it never assigns the same value to two different domain elements.
- **Non-decreasing Function:** A function is non-decreasing if for all \( x_1 < x_2 \), \( f(x_1) \leq f(x_2) \).
For further learning, consider exploring graphing tools to visualize these functions.
Weather Data: 78°F, Mostly Sunny
---
This content is tailored for students studying mathematics, specifically in algebra and precalculus, who need to understand function properties and finding inverses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76c19111-0832-474a-9997-f0da2ac47ca4%2Fc6ec643f-6bff-4e27-b4dd-bc6fb507b5c0%2Fntz6p9c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here’s the transcription suitable for an educational website:
---
### Problem Statement
**Given Function:**
\[ f(x) = (x + 4)^2 \]
#### Problem 1:
**Find a domain on which \( f \) is one-to-one and non-decreasing.**
\[ \boxed{\quad \quad \quad \quad \quad \quad} \]
#### Problem 2:
**Find the inverse of \( f \) restricted to this domain.**
\[ f^{-1}(x) = \boxed{\quad \quad \quad \quad} \]
---
Note: Since this problem involves both the properties of functions and the concept of inverse functions, a good grasp of these topics is beneficial.
- **One-to-one Function:** A function is one-to-one if it never assigns the same value to two different domain elements.
- **Non-decreasing Function:** A function is non-decreasing if for all \( x_1 < x_2 \), \( f(x_1) \leq f(x_2) \).
For further learning, consider exploring graphing tools to visualize these functions.
Weather Data: 78°F, Mostly Sunny
---
This content is tailored for students studying mathematics, specifically in algebra and precalculus, who need to understand function properties and finding inverses.
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