For the Given Functions F and G, Find the Requested $$f ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }$$

question 71

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $$f ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }$$
Find $\mathrm { f } \cdot \mathrm { g }$ .

• A) \(( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { 2 \mathrm { x } + 14 } } { \mathrm { x } } ; \{ \mathrm { x } \mid \mathrm { x } \geq - 7 , \mathrm { x } \neq 0 \}\)
• B) \(( f \cdot g ) ( x ) = \frac { 2 \sqrt { x + 7 } } { x } ; \{ x \mid x \geq - 7 , x \neq 0 \}\)
• C) \(( f \cdot g ) ( x ) = \sqrt { \frac { 9 } { x } } ; \{ x \mid x \neq 0 \}\)
• D) \(( f \cdot g ) ( x ) = \sqrt { \frac { 2 x + 14 } { x } } ; \{ x \mid x \geq - 7 , x \neq 0 \}\)

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Definitions:

Humanistic

An approach in psychology that emphasizes empathy and stresses the good in human behavior, focusing on the potential for self-growth.

Psychodynamic

A psychological approach that emphasizes the study of the psychological forces underlying human behavior, feelings, and emotions, and how they might relate to early experience.

Biological

Pertaining to the processes and phenomena of living organisms, or in a broader sense, related to the life sciences.

Self-regulation Theory

A theory that focuses on individuals' control of their own behavior and emotions, aiming for goal achievement.