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

Question

Quizplus · Accepted Answer

The equation $y = 3 \tan (2x - 1)$ can be rearranged to solve for $x$ as $x = \frac{1}{2} + \frac{1}{2} \arctan \frac{y}{3}$, which matches option C.

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