Solve the Equation for X, Where X Is Restricted to the Given

question 451

Multiple Choice

Solve the equation for x, where x is restricted to the given interval.
- $y = 3 \tan 2 x - 1$ , for $x$ in $\left( - \frac { \pi } { 4 } , \frac { \pi } { 4 } \right)$

• A) \(x = \frac { 1 } { 2 } \arctan \frac { y + 1 } { 3 }\)
• B) \(x = 2 \arctan \frac { y + 1 } { 3 }\)
• C) \(x = \frac { 1 } { 2 } \arctan ( 3 y + 3 )\)
• D) \(x = 2 \arctan ( 3 y + 3 )\)

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Definitions:

Conscious Experience

The awareness of internal or external existence, including thoughts, feelings, and perceptions.

James-Lange Theory

The James-Lange Theory proposes that emotions result from the interpretation of bodily responses to external stimuli, before the emotion is experienced.

Conscious Experience

The awareness of the self, one's thoughts, and the environment, forming the basis of subjectivity and personal experience.

Autonomic Arousal

The activation of the autonomic nervous system, governing involuntary physiological responses to stimuli.