What would the domain restrictions have to be to find the inverse of the following; f(x) =Cos () O [0, 27] O [0, 1] [0, 플] enovo
What would the domain restrictions have to be to find the inverse of the following; f(x) =Cos () O [0, 27] O [0, 1] [0, 플] enovo
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![**Title: Understanding Domain Restrictions to Find the Inverse**
**Question:**
What would the domain restrictions have to be to find the inverse of the following function?
\[ f(x) = \frac{3}{2} \cos\left(\frac{x}{2}\right) \]
**Options:**
- \(\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]\)
- \([0, 2\pi]\)
- \([0, \pi]\)
- \([- \pi, \pi]\)
- \([0, \frac{\pi}{2}]\)
**Explanation:**
To find the inverse of a cosine function, the function must be restricted to an interval where it is one-to-one. The cosine function is typically considered one-to-one on the interval \([0, \pi]\) for the purpose of finding an inverse. The question provides different intervals from which the correct one must be chosen.
**Note:** Understanding the properties and behavior of trigonometric functions, such as the cosine function, is crucial when determining domain restrictions for inverses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7eb4d7b3-cbb9-425b-9064-1274d5c24cf4%2F403c3bae-c489-4d55-9a10-53604b81667f%2F5vctjzl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Domain Restrictions to Find the Inverse**
**Question:**
What would the domain restrictions have to be to find the inverse of the following function?
\[ f(x) = \frac{3}{2} \cos\left(\frac{x}{2}\right) \]
**Options:**
- \(\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]\)
- \([0, 2\pi]\)
- \([0, \pi]\)
- \([- \pi, \pi]\)
- \([0, \frac{\pi}{2}]\)
**Explanation:**
To find the inverse of a cosine function, the function must be restricted to an interval where it is one-to-one. The cosine function is typically considered one-to-one on the interval \([0, \pi]\) for the purpose of finding an inverse. The question provides different intervals from which the correct one must be chosen.
**Note:** Understanding the properties and behavior of trigonometric functions, such as the cosine function, is crucial when determining domain restrictions for inverses.
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