What is the domain of the function [tex]$y = \sqrt{x + 6} - 7$[/tex]?

A. [tex]$x \geq -7$[/tex]
B. [tex]$x \geq -6$[/tex]
C. [tex]$x \geq 6$[/tex]
D. [tex]$x \geq 7$[/tex]



Answer :

To determine the domain of the function \( y = \sqrt{x + 6} - 7 \), let's follow these steps:

1. Identify the expression inside the square root: The function involves a square root, which is \( \sqrt{x + 6} \).

2. Determine the condition for the square root: The square root function is defined only when the radicand (the expression inside the square root) is non-negative. In other words, the expression inside the square root must be greater than or equal to zero.

[tex]\[ x + 6 \geq 0 \][/tex]

3. Solve the inequality for \( x \):

[tex]\[ x + 6 \geq 0 \][/tex]

Subtract 6 from both sides:

[tex]\[ x \geq -6 \][/tex]

Based on this solution, the domain of the function \( y = \sqrt{x + 6} - 7 \) is all values of \( x \) such that \( x \geq -6 \).

Thus, the correct answer is:

[tex]\[ x \geq -6 \][/tex]