#### Answer

$g^{-1}(t) = -\frac{t-6}{2}$

#### Work Step by Step

$g(t) = -2t+6$
Let $g(t) = y$
$y = -2t + 6$
Swap the variables $t$ and $y$ and then solve for $y$ to find the inverse:
$t = -2y + 6$
$t - 6 = -2y$
$y = -\frac{t-6}{2}$
$g^{-1}(t) = -\frac{t-6}{2}$