Answered

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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 DefinedAx 0Bx 6Cx 3Dx 6 class=

Sagot :

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]

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