Answer
$g^{-1}(x) = -\frac{x-20}{4}$
Work Step by Step
$g(x) =-4x+20$
Let $g(x) = y$
$y = -4x+20$
Swap the $x$ and $y$ variable to find the inverse:
$x = -4y+20$
$x - 20 = -4y$
$y = -\frac{x-20}{4}$
$g^{-1}(x) = -\frac{x-20}{4}$