To determine the domain of the function [tex]\( y = \sqrt{x + 6} - 7 \)[/tex], we need to consider the conditions under which the function is defined.
The function includes a square root, [tex]\( \sqrt{x + 6} \)[/tex]. The square root function is only defined for non-negative values inside the root. Therefore, the expression inside the square root must be greater than or equal to zero:
[tex]\[ x + 6 \geq 0. \][/tex]
Next, we solve this inequality for [tex]\( x \)[/tex]:
[tex]\[
x + 6 \geq 0 \quad \Rightarrow \quad x \geq -6.
\][/tex]
Thus, the domain of the function [tex]\( y = \sqrt{x + 6} - 7 \)[/tex] is [tex]\( x \geq -6 \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{x \geq -6} \][/tex]
