For the Given Functions F and G, Find the Requested $\text { Find } \frac { \mathrm { f } } { \mathrm { g } } \text {. }$

question 70

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
-f(x) = 5x + 4; g(x) = 5x - 3 $\text { Find } \frac { \mathrm { f } } { \mathrm { g } } \text {. }$

• A) \(\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 3 } { 5 \mathrm { x } + 4 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 3 } { 5 } \right\}\)
• B) \(\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 3 } { 5 x + 4 } ; \left\{ x \mid x \neq - \frac { 4 } { 5 } \right\}\)
• C) \(\left( \frac { f } { g } \right) ( x ) = \frac { 5 x + 4 } { 5 x - 3 } ; \left\{ x \mid x \neq \frac { 3 } { 5 } \right\}\)
• D) \(\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } + 4 } { 5 \mathrm { x } - 3 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 4 } { 5 } \right\}\)

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Definitions:

New York Longitudinal Study

A research project that began in the 1950s tracking the temperamental characteristics of infants and how these traits relate to personality development.

Temperamental Category

A classification in psychology that describes inherent personality traits and behavior tendencies that are observable in infancy and assumed to be biologically based.

Mixed Temperament

A combination of multiple temperament traits in an individual, showing behavioral characteristics that are not dominated by a single temperament type.

Basic Temperamental Categories

The classification of fundamental personality traits that are often identified early in life, including factors like activity levels, emotional reactivity, and sociability.