Question
Determine the domain of the following function. \( y=\sqrt{x-6} \) The domain is \( \square \). (Type your answer in interval notation.)
Ask by Boyd Pierce. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain is [6, ∞).
Solution
The expression under the square root must be greater than or equal to zero since you cannot take the square root of a negative number in the set of real numbers. Set up the inequality:
x - 6 ≥ 0
Now solve for x:
x ≥ 6
In interval notation, the domain of the function is [6, ∞).
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Simplify this solution Extra Insights
To determine the domain of the function \( y=\sqrt{x-6} \), we need the expression under the square root to be non-negative. This means \( x - 6 \geq 0 \). Solving this inequality gives us \( x \geq 6 \). Therefore, the domain in interval notation is \( [6, \infty) \). Remember, the square root function only accepts zero or positive numbers, so it’s crucial to identify those values to ensure the function outputs real numbers! Function domains can sometimes be puzzling, but just stick to the rules of arithmetic—works like a charm!
