Let's carefully determine the domain of the function [tex]\( y = \sqrt{x - 5} - 1 \)[/tex].
1. Analyze the function:
The function involves a square root. For a square root to produce a real number, the expression inside it must be non-negative.
2. Set up the inequality:
The expression inside the square root is [tex]\( x - 5 \)[/tex]. This must be non-negative:
[tex]\[
x - 5 \geq 0
\][/tex]
3. Solve the inequality:
Solve for [tex]\( x \)[/tex]:
[tex]\[
x \geq 5
\][/tex]
4. Conclusion:
The domain of the function [tex]\( y = \sqrt{x - 5} - 1 \)[/tex] consists of all [tex]\( x \)[/tex]-values that satisfy [tex]\( x \geq 5 \)[/tex].
Thus, the correct inequality is:
[tex]\[
\boxed{x \geq 5}
\][/tex]
