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What is the domain of the function [tex]\( y = \sqrt{x+6} \)[/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 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]