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:

Self Archetype

In Jungian psychology, represents the unification of the consciousness and unconsciousness in an individual, embodying the sense of wholeness and integration.

Equilibrium

A state of physical balance or a stable situation in which forces cancel one another.

Forces

Influences or powers that can cause changes in physical motion or in social or psychological dynamics.

Personality

Encompasses the characteristic patterns of thoughts, feelings, and behaviors that make a person unique.