IDNLearn.com: Where your questions meet expert advice and community insights. Join our platform to receive prompt and accurate responses from experienced professionals in various fields.

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]


Sagot :

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]