#### Answer

$f^{-1}(x) = \frac{x + 2}{4 - 3x}$

#### Work Step by Step

$f(x) = \frac{4x - 2}{3x + 1}$
$y = \frac{4x - 2}{3x + 1}$
y(3x + 1) = 4x - 2
3xy + y = 4x - 2
y + 2 = 4x - 3xy
y + 2 = x(4 - 3y)
$x = \frac{y + 2}{4 - 3y}$
$f^{-1}(x) = \frac{x + 2}{4 - 3x}$