Find the domain of the following function. f(x,y) = cos X-2 .y + 1
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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Question
![**Find the Domain of the Following Function**
Given function:
\[ f(x, y) = \cos\left(\frac{x - 2}{y + 1}\right) \]
Determine the domain of the function.
**Select the Correct Choice Below and Fill in Any Answer Boxes Within Your Choice:**
- **A.** \((x, y): x \neq \_\)
*(Use a comma to separate answers as needed.)*
- **B.** \((x, y): y \neq \_\)
*(Use a comma to separate answers as needed.)*
- **C.** \((x, y): x \neq \_\) and \(y \neq \_\)
*(Use a comma to separate answers as needed.)*
- **D.** \(\mathbb{R}^2\)
**Explanation:**
To determine the domain, consider where the expression inside the cosine function is defined. Since it's a fraction \(\frac{x - 2}{y + 1}\), the denominator cannot be zero. Thus, \(y + 1 \neq 0\), or equivalently, \(y \neq -1\). The set of all possible \((x, y)\) values where \(y \neq -1\) forms the domain of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ade5d6c-ff37-4df2-b1de-522b52697cc9%2F18fc4649-a1ab-4e18-a4d7-1f2532b69889%2Fikmq5tm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Domain of the Following Function**
Given function:
\[ f(x, y) = \cos\left(\frac{x - 2}{y + 1}\right) \]
Determine the domain of the function.
**Select the Correct Choice Below and Fill in Any Answer Boxes Within Your Choice:**
- **A.** \((x, y): x \neq \_\)
*(Use a comma to separate answers as needed.)*
- **B.** \((x, y): y \neq \_\)
*(Use a comma to separate answers as needed.)*
- **C.** \((x, y): x \neq \_\) and \(y \neq \_\)
*(Use a comma to separate answers as needed.)*
- **D.** \(\mathbb{R}^2\)
**Explanation:**
To determine the domain, consider where the expression inside the cosine function is defined. Since it's a fraction \(\frac{x - 2}{y + 1}\), the denominator cannot be zero. Thus, \(y + 1 \neq 0\), or equivalently, \(y \neq -1\). The set of all possible \((x, y)\) values where \(y \neq -1\) forms the domain of the function.
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