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:

Depression

A mental health disorder that is marked by persistent feelings of sadness, apathy, and loss of interest, significantly affecting daily functioning.

Mood Disorders

A category of psychiatric disorders characterized by the disturbance of a person's mood, leading to periods of depression or elevated mood.

Imagined Loss

Freudian theory that the individual unconsciously interprets all types of loss events (e.g., job loss) in terms of grief, thereby raising the risk for depression.