Appendix A - Section A.2 - The Inverse of a Function - A.2 Problem Set - Page 496: 21

$f^{-1}(x) = \frac{1-x}{3x-2}$

$f(x) = \frac{2x+1}{3x+1}$ Let $f(x) = y$ $y = \frac{2x+1}{3x+1}$ $x = \frac{2y+1}{3y+1}$ $3xy + x = 2y + 1$ $3xy - 2y = 1 -x$ $y(3x -2) = 1-x$ $y = \frac{1-x}{3x-2}$ $f^{-1}(x) = \frac{1-x}{3x-2}$