To find the domain of the function [tex]\( y = \sqrt{x + 6} \)[/tex], you need to ensure that the expression inside the square root is non-negative because the square root of a negative number is not defined in the set of real numbers.
Here’s a step-by-step solution:
1. Analyze the condition inside the square root:
The function is given as [tex]\( y = \sqrt{x + 6} \)[/tex]. We need to ensure that the expression inside the square root, [tex]\( x + 6 \)[/tex], is non-negative.
2. Set up the inequality:
[tex]\[
x + 6 \geq 0
\][/tex]
3. Solve the inequality for [tex]\( x \)[/tex]:
To solve [tex]\( x + 6 \geq 0 \)[/tex], we subtract 6 from both sides:
[tex]\[
x \geq -6
\][/tex]
Thus, the domain of the function [tex]\( y = \sqrt{x + 6} \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \geq -6 \)[/tex].
Therefore, the correct answer is:
[tex]\[ x \geq -6 \][/tex]
