A Company's Profit $P$ For Producing $x$ Units Is Given By $P ( x ) = 47 x - 5736$

question 40

Multiple Choice

A company's profit $P$ for producing $x$ units is given by $P ( x ) = 47 x - 5736$ . Find the inverse function $P ^ { - 1 } ( x )$ and explain what it represents. Describe the domains of $P ( x )$ and $P ^ { - 1 } ( x )$ .

• A) \(P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }\) , \(P ^ { - 1 } ( x )\) represents the number of units that must be sold to obtain the profit of \(x\) .Domain of \(P ( x ) : [ 0,10 )\) , Domain of \(P ^ { - 1 } ( x ) : [ - 5736 , \infty )\)
• B) \(P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }\) , \(P ^ { - 1 } ( x )\) represents the number of units that must be sold to obtain the profit of \(x\) .Domain of \(P ( x ) : [ 0 , \infty )\) , Domain of \(P ^ { - 1 } ( x ) : [ - 5736,5736 )\)
• C) \(P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }\) , \(P ^ { - 1 } ( x )\) represents the number of units that must be sold to obtain the profit of \(x\) .Domain of \(P ( x ) : [ 0 , \infty )\) , Domain of \(P ^ { - 1 } ( x ) : [ - 5736 , \infty )\)
• D) \(P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }\) , \(P ^ { - 1 } ( x )\) represents the number of units that must be sold to obtain the profit of \(x\) .Domain of \(P ( x ) : [ 1 , \infty )\) , Domain of \(P ^ { - 1 } ( x ) : [ - 5736 , \infty )\)
• E) \(P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }\) , \(P ^ { - 1 } ( x )\) represents the number of units that must be sold to obtain the profit of \(x\) .Domain of \(P ( x ) : [ 0 , \infty )\) , Domain of \(P ^ { - 1 } ( x ) : [ - 5736,47 )\)

Understand the difference between place and response learning in animals.

Grasp the foundational theories of Tolman, Dickinson, and Seligman within cognitive and behavioral psychology contexts.

Recognize how external stimuli and internal cognitions influence behavior and learning.

Understand the role of habituation, expectancy, and association in controlling behavior.

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Definitions:

Systematic Desensitization

A therapeutic method used to help individuals overcome phobias and anxiety disorders by gradually exposing them to the feared object or situation in a controlled and hierarchical manner.

Biofeedback

A technique that teaches individuals to control physiological processes such as heart rate or blood pressure by providing real-time feedback.

Self-monitoring

The process where individuals pay attention to their own behavior and its effects on others.

Observation

The act of closely monitoring or watching phenomena as they occur in order to collect data or make inferences.