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Determine the domain of the function [tex]\( y = \sqrt{x - 5} - 1 \)[/tex].

A. [tex]\( x \geq -5 \)[/tex]
B. [tex]\( x \geq -1 \)[/tex]
C. [tex]\( x \geq 1 \)[/tex]
D. [tex]\( x \geq 5 \)[/tex]

Sagot :

GinnyAnswer
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]
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