Question

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

Explanation:

Step1: Recall domain of square root

For $\sqrt{u}$, $u\geq0$. Here, $u = x - 6$.

Step2: Solve inequality

Set $x - 6\geq0$. Add 6 to both sides: $x\geq6$. So domain is $6\leq x<\infty$.

Answer:

$6 \leq x < \infty$ (the option with this text, e.g., if it's the third option, state: "The third option: $6 \leq x < \infty$")