Answer
$f^{-1}(x) = \frac{2-x}{5x-3}$
Work Step by Step
$f(x) = \frac{3x+2}{5x+1}$
Let $f(x) = y$
$y = \frac{3x+2}{5x+1}$
$x = \frac{3y+2}{5y+1}$
$5xy + x = 3y + 2$
$5xy - 3y = 2 -x$
$y(5x - 3) = 2-x$
$y = \frac{2-x}{5x-3}$
$f^{-1}(x) = \frac{2-x}{5x-3}$
