Determine the Domain of the Function $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

question 54

Multiple Choice

Determine the domain of the function.
- $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

• A) \(\{ x \mid x \neq 3 , x \neq - 3 \text {, and } x \neq - 5 \}\)
• B) \(\{ x \mid x \neq 3 \text { and } x \neq - 5 \}\)
• C) \(\{ x \mid x \neq - 3 \text { and } x \neq 5 \}\)
• D) \(\{ x \mid x \text { is a real number } \}\)

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Definitions:

Cerebral Cortex

This refers to the brain's cerebrum's outer neural tissue, instrumental in controlling memory, cognition, consciousness, thought, language, perception, and attention.

Hemisphere

Half of a spherical or roughly spherical structure, especially one of the halves of the brain.

Caudate Nucleus

A curved, elongated nucleus located within the brain, playing a key role in various functions including motor processing, learning, memory, and emotion regulation.

Corpus Striatum

Caudate nucleus, putamen, and globus pallidus; so-named because of the striations caused by intermixing of gray and white matter, which result from the number of tracts crossing the anterior portion of the corpus striatum.