Determine the X Values That Cause the Function to Be $$f ( x ) = \frac { \sqrt { x + 9 } } { ( 2 x + 3 ) ( x - 2 ) }$$

question 221

Multiple Choice

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative.
- $$f ( x ) = \frac { \sqrt { x + 9 } } { ( 2 x + 3 ) ( x - 2 ) }$$

• A) (a) \(\left\{ - 9,2 , - \frac { 3 } { 2 } \right\}\), (b) \(( x , - 9 )\), (c) \(\left( - 9 , - \frac { 3 } { 2 } \right) \cup ( 2 , \infty )\), (d) \(\left( - \frac { 3 } { 2 } , 2 \right)\)
• B) (a) \(\{ - 9 \}\), (b) \(\left\{ 2 , - \frac { 3 } { 2 } \right\} \cup ( \infty , - 9 )\), (c) \(\left( - 9 , - \frac { 3 } { 2 } \right) \cup ( 2 , \infty )\), (d) \(\left( - \frac { 3 } { 2 } , 2 \right)\)
• C) (a) \(\{ - 9 \}\), (b) \(\left\{ 2 , - \frac { 3 } { 2 } \right\} \cup ( \infty , - 9 ) , ( c ) \left( - \frac { 3 } { 2 } , 2 \right)\), (d) \(\left( - 9 , - \frac { 3 } { 2 } \right) \cup ( 2 , \infty )\)
• D) (a) \(\left\{ - 9,2 , - \frac { 3 } { 2 } \right\}\), (b) \(( * , - 9 ) , ( \mathrm { c } ) \left( - \frac { 3 } { 2 } , 2 \right)\), (d) \(\left( - 9 , - \frac { 3 } { 2 } \right) \cup ( 2 , \infty )\)

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Definitions:

Average Fixed Cost

is calculated by dividing the total fixed costs of production by the quantity of output produced, showing the cost per unit of output.

Total Variable Cost

The sum of all variable expenses related to the production of goods or services, which vary with the level of output.

Total Cost

The sum of all costs incurred by a business in producing a certain quantity of a good or service.

Marginal Cost

The cost change associated with making an additional unit of a product, emphasizing the incremental expense in production activities.