Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Finding the Domain of a Function
**Problem Statement:**
Find the domain of the following function.
\[ g(x) = \frac{9}{\sqrt{10 + x}} \]
**Solution:**
To find the domain of the function \( g(x) = \frac{9}{\sqrt{10 + x}} \), we need to identify all values of \( x \) for which the function is defined.
1. **Denominator Constraint**:
- The denominator \(\sqrt{10 + x}\) must be non-zero and defined. Since the square root function is only defined for non-negative values, we must have:
\[
10 + x > 0
\]
- Solving this inequality:
\[
x > -10
\]
2. **Conclusion**:
- The function \( g(x) = \frac{9}{\sqrt{10 + x}} \) is defined for all \( x \) values greater than -10.
**Interval Notation**:
Thus, the domain of the function \( g(x) \) in interval notation is:
\[ (-10, \infty) \]
**Final Answer**:
\[
\text{The domain is } \boxed{(-10, \infty)}
\]
Please type your answer in interval notation, as indicated in the problem statement.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c22293a-3ae6-4ac2-9c37-c12acd82a0e8%2F75bb4fa1-b7c2-40ca-9982-deb560355b50%2Fth5vu2x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Domain of a Function
**Problem Statement:**
Find the domain of the following function.
\[ g(x) = \frac{9}{\sqrt{10 + x}} \]
**Solution:**
To find the domain of the function \( g(x) = \frac{9}{\sqrt{10 + x}} \), we need to identify all values of \( x \) for which the function is defined.
1. **Denominator Constraint**:
- The denominator \(\sqrt{10 + x}\) must be non-zero and defined. Since the square root function is only defined for non-negative values, we must have:
\[
10 + x > 0
\]
- Solving this inequality:
\[
x > -10
\]
2. **Conclusion**:
- The function \( g(x) = \frac{9}{\sqrt{10 + x}} \) is defined for all \( x \) values greater than -10.
**Interval Notation**:
Thus, the domain of the function \( g(x) \) in interval notation is:
\[ (-10, \infty) \]
**Final Answer**:
\[
\text{The domain is } \boxed{(-10, \infty)}
\]
Please type your answer in interval notation, as indicated in the problem statement.
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