To determine the domain of the function [tex]\( y = \sqrt{x - 10} \)[/tex], we need to find all possible values of [tex]\( x \)[/tex] for which the function is defined.
The square root function [tex]\( \sqrt{u} \)[/tex] is defined only when the argument [tex]\( u \)[/tex] is non-negative because the square root of a negative number is not a real number.
For the function [tex]\( y = \sqrt{x - 10} \)[/tex], the argument inside the square root is [tex]\( x - 10 \)[/tex]. Therefore, we require that:
[tex]\[
x - 10 \geq 0
\][/tex]
To solve this inequality, we add 10 to both sides:
[tex]\[
x \geq 10
\][/tex]
Hence, the function [tex]\( y = \sqrt{x - 10} \)[/tex] is defined for all [tex]\( x \)[/tex] such that [tex]\( x \geq 10 \)[/tex].
Therefore, the domain of the function is:
[tex]\[
x \geq 10
\][/tex]
This corresponds to choice:
A [tex]\( x \geq 10 \)[/tex].
