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

Which inequality represents all values of x for which the product below is defined-example-1
User Taya
by
2.9k points

1 Answer

20 votes
20 votes

Solution

Step 1:

Write the expression:


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

Step 2:


\begin{gathered} Apply\text{ the rule below:} \\ √(a)\text{ . }√(b)\text{ = }√(ab) \end{gathered}

Step 3:


\begin{gathered} \sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}} \\ \\ √((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}

User Jeff Widman
by
3.1k points