To determine the domain of the function [tex]\( y = 2 \sqrt{x - 5} \)[/tex], we need to consider the constraint imposed by the square root. The expression inside the square root must be non-negative because the square root of a negative number is not defined in the set of real numbers.
The function [tex]\( y = 2 \sqrt{x - 5} \)[/tex] involves the square root of [tex]\( x - 5 \)[/tex], so we set up the following inequality to ensure the expression inside the square root is non-negative:
[tex]\[ x - 5 \geq 0 \][/tex]
Now, solve this inequality for [tex]\( x \)[/tex]:
[tex]\[ x \geq 5 \][/tex]
This means that [tex]\( x \)[/tex] must be greater than or equal to 5 for the function to be defined. Therefore, the domain of the function [tex]\( y = 2 \sqrt{x - 5} \)[/tex] is:
[tex]\[ x \geq 5 \][/tex]
Thus, the correct answer is:
[tex]\[ x \geq 5 \][/tex]
