Solution
Step 1:
Write the expression:
[tex]\sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}}[/tex]
Step 2:
[tex]\begin{gathered} Apply\text{ the rule below:} \\ \sqrt{a}\text{ . }\sqrt{b}\text{ = }\sqrt{ab} \end{gathered}[/tex]
Step 3:
[tex]\begin{gathered} \sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}} \\ \\ \sqrt{(x-6)(x+3)} \\ \\ For\text{ the function to be defined} \\ (x\text{ - 6\rparen\lparen x + 3\rparen }\ge\text{ 0} \end{gathered}[/tex]
Step 4:
[tex]x\le \:-3\quad \mathrm{or}\quad \:x\ge \:6\:[/tex]
Final answer
[tex]\begin{gathered} Option\text{ D } \\ x\text{ }\ge\text{ 6} \end{gathered}[/tex]
