Question

Which inequality represents all values of x for which the product below is defined?A.x 0B.x 6C.x -3D.x 6

Answer 1

Solution

Step 1:

Write the expression:

$\sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}}$

Step 2:

$\begin{gathered} Apply\text{ the rule below:} \\ \sqrt{a}\text{ . }\sqrt{b}\text{ = }\sqrt{ab} \end{gathered}$

Step 3:

$\begin{gathered} \sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}} \\ \\ \sqrt{(x-6)(x+3)} \\ \\ For\text{ the function to be defined} \\ (x\text{ - 6\rparen\lparen x + 3\rparen }\ge\text{ 0} \end{gathered}$

Step 4:

$x\le \:-3\quad \mathrm{or}\quad \:x\ge \:6\:$

Final answer

$\begin{gathered} Option\text{ D } \\ x\text{ }\ge\text{ 6} \end{gathered}$