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What is the domain of the function [tex]\( y = 2 \sqrt{x-6} \)[/tex]?
A. [tex]\(-\infty \ \textless \ x \ \textless \ \infty\)[/tex] B. [tex]\(0 \leq x \ \textless \ \infty\)[/tex] C. [tex]\(3 \leq x \ \textless \ \infty\)[/tex] D. [tex]\(6 \leq x \ \textless \ \infty\)[/tex]
To determine the domain of the function [tex]\( y = 2 \sqrt{x - 6} \)[/tex], we need to ensure that the expression inside the square root is non-negative. The square root function is only defined for non-negative values, meaning that the input must be zero or positive.
Given the function [tex]\( y = 2 \sqrt{x - 6} \)[/tex], the expression inside the square root is [tex]\( x - 6 \)[/tex]. So, we need:
[tex]\[ x - 6 \geq 0 \][/tex]
Solving this inequality for [tex]\( x \)[/tex] gives:
[tex]\[ x \geq 6 \][/tex]
This means that the function is defined for all values of [tex]\( x \)[/tex] starting from 6 and extending to infinity. In interval notation, we write this as:
[tex]\[ 6 \leq x < \infty \][/tex]
Therefore, the correct option that represents the domain of the function [tex]\( y = 2 \sqrt{x - 6} \)[/tex] is:
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