https://file.aiquickdraw.com/mathbot/file/1727888678430pakjbuh9.jpg

The question asks for the domain of the function \( g(x) = \sqrt{x + 14} \) in interval notation.

To find the domain of a square root function, we need the expression inside the square root to be non-negative because the square root of a negative number is not defined in the set of real numbers.

So, we set the inside of the square root greater than or equal to zero:
\[
x + 14 \geq 0
\]
Solving for \(x\):
\[
x \geq -14
\]
Therefore, the domain of \(g(x)\) is all values of \(x\) greater than or equal to \(-14\).

In interval notation, the domain is:
\[
[-14, \infty)
\]

Would you like further details or have any questions? 

Here are some related questions you might find helpful:
1. What is the domain of \( g(x) = \sqrt{2x + 5} \)?
2. How do you find the domain of a function involving square roots?
3. What is the range of the function \( g(x) = \sqrt{x + 14} \)?
4. Can you explain the difference between domain and range?
5. What happens to the domain if the function involves a negative square root?

**Tip:** For square root functions, always check that the expression inside the square root is non-negative to ensure the domain is valid.

Give the domain of g(x) = √(x + 14) in interval notation.

Learn how to determine the domain of the function g(x) = √(x + 14) in interval notation. This problem explores the conditions under which the expression inside the square root is non-negative. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation