Question
State the domain of the given function. \( f(x)=\sqrt{x+6} \)
Ask by Mejia Pierce. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain of \( f(x) = \sqrt{x+6} \) is all real numbers greater than or equal to -6, which is \([-6, \infty)\).
Solution
1. The function is given by \( f(x)=\sqrt{x+6} \).
2. The expression inside the square root, \( x+6 \), must be non-negative, so we set up the inequality:
\[
x+6 \geq 0
\]
3. Solving the inequality:
\[
x \geq -6
\]
4. Therefore, the domain of \( f(x) \) is:
\[
[-6, \infty)
\]
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Simplify this solution Beyond the Answer
For the function \( f(x) = \sqrt{x+6} \) to be defined, the expression inside the square root must be non-negative. This means we need \( x + 6 \geq 0 \). Solving this inequality gives us \( x \geq -6 \). Therefore, the domain of the function is all real numbers \( x \) such that \( x \) is greater than or equal to \(-6\). In interval notation, this is written as \([-6, \infty)\). So grab your math gear and get ready to explore functions, because knowing how to find a domain is like having a treasure map for your mathematical adventures!
