Find the Indicated Function and Write Its Domain in Interval $$s ( x ) = \frac { x - 4 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 4 - x } , \left( \frac { s } { t } \right) ( x ) = ?$$

question 227

Multiple Choice

Find the indicated function and write its domain in interval notation.
- $$s ( x ) = \frac { x - 4 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 4 - x } , \left( \frac { s } { t } \right) ( x ) = ?$$

• A) \(- \frac { ( x - 4 ) ^ { 2 } } { ( x - 6 ) ^ { 2 } ( x + 6 ) } ; ( - \infty , - 6 ) \cup ( - 6,4 ) \cup ( 4,6 ) \cup ( 6 , \infty )\)
• B) \(- \frac { 1 } { x + 6 } ; ( - \infty , - 6 ) \cup ( - 6 , \infty )\)
• C) \(- \frac { ( x - 4 ) ^ { 2 } } { ( x - 6 ) ^ { 2 } ( x + 6 ) } ; ( - \infty , - 6 ) \cup ( 6 , \infty )\)
• D) \(- \frac { 1 } { x + 6 } ; ( - \infty , - 6 ) \cup ( - 6,4 ) \cup ( 4,6 ) \cup ( 6 , \infty )\)

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Definitions:

EEG Patterns

Distinctive electrical activity patterns of the brain, as recorded by electroencephalography, that can indicate normal or abnormal brain function.

REM Sleep

A phase of sleep characterized by rapid eye movements, low muscle tone, and vivid dreams, playing a crucial role in emotional regulation and memory consolidation.

High-Frequency Waves

Brain wave patterns, usually associated with states of alertness and cognitive activity, measured in hertz.

Slave Oscillators

Components within larger synchronized systems, such as biological clocks, that follow the rhythm dictated by a master oscillator.