Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 279: 16

$x=\frac{1}{2} (arctan(y)+1)$

$y=tan(2x-1)$ Need to solve $x$ in order to find this use inverse trigonometric function. $2x-1=arctan(y)$ $2x=arctan(y)+1$ Divide by 2 on both sides. $x=\frac{1}{2} (arctan(y)+1)$ Hence, $x=\frac{1}{2} (arctan(y)+1)$