Determine I) the Domain of the Function, Ii) the Range $$f ( x ) = \frac { 4 } { 6 x + 5 }$$

question 346

Multiple Choice

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of
the inverse.
- $$f ( x ) = \frac { 4 } { 6 x + 5 }$$

• A) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 2 } { 3 } \right\} , R = \left\{ y \mid y \neq \frac { 4 } { 5 } \right\}\);
• \(f ^ { - 1 } ( x ) : D = \left\{ x \mid x \neq \frac { 4 } { 5 } \right\} , R = \left\{ y \mid y \neq \frac { 2 } { 3 } \right\}\)
• B) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 5 } { 6 } \right\} R = \{ y \mid y \neq - 5 \}\);
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 5 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 5 } { 6 } \right\} \right.\)
• C) \(f ( x )\) : \(D\) is all real numbers, \(R\) is all real number:
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } )\) : \(\mathrm { D }\) is all real numbers, \(R\) is all real numbe
• D) \(f ( x ) : D = \left\{ x \mid x \neq - \frac { 5 } { 6 } \right\} , R = \{ y \mid y \neq 0 \}\)
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \left\{ \mathrm { y } \mid \mathrm { y } \neq - \frac { 5 } { 6 } \right\}\] ;

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Definitions:

Sensory Pathway

Nerves coming from the sensory organs to the CNS consisting of afferent neurons.

Afferent Neurons

Nerve cells that carry sensory information from the body's tissues and organs towards the central nervous system.

Efferent Neurons

Nerve cells that convey impulses away from the central nervous system to effectors, such as muscles or glands.

Synaptic Gap

The tiny space between neurons across which neurotransmitters travel to carry signals from one neuron to another.