Question

what is the domain of the function $y = 2sqrt{x - 6}$?\
$\bigcirc -\infty < x < \infty$\
$\bigcirc 0 \leq x < \infty$\
$\bigcirc 3 \leq x < \infty$\
$\bigcirc 6 \leq x < \infty$

Explanation:

Step1: Recall domain of square root function

For a square root function \(\sqrt{u}\), the expression inside the square root (\(u\)) must be non - negative, i.e., \(u\geq0\).
In the function \(y = 2\sqrt{x - 6}\), the expression inside the square root is \(x-6\). So we set up the inequality \(x - 6\geq0\).

Step2: Solve the inequality

To solve \(x - 6\geq0\), we add 6 to both sides of the inequality.
\(x-6 + 6\geq0 + 6\)
Which simplifies to \(x\geq6\). In interval notation, this is \(6\leq x<\infty\).

Answer:

\(6\leq x<\infty\) (the option: \(6\leq x<\infty\))