Find the Domain of the Rational Function $$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 8 x + 12 }$$

question 23

Multiple Choice

Find the domain of the rational function.
- $$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 8 x + 12 }$$

• A) domain of \(f : ( \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )\)
• B) domain of \(f : ( \infty , 0 ) \cup ( 0 , \infty )\)
• C) domain of \(f : ( \infty , 2 ) \cup ( 2,6 ) \cup ( 6 , \infty )\)
• D) domain of \(f : ( \infty , - 6 ) \cup ( - 6 , - 2 ) \cup ( - 2 , \infty )\)

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Definitions:

Long Run

A period in economics where all factors of production and costs are variable, allowing full adjustment to any change in economic conditions.

Economies of Scale

The cost advantages that enterprises obtain due to their scale of operation, leading to a reduced cost per unit of output.

Average Variable Cost Curve

A graphical representation that shows how the average variable cost of production varies with the level of output.

Long-run Average Total Cost

This refers to the per unit cost of production when all inputs can be adjusted, conceived for analyzing the scale of production without the constraint of fixed capital.