Answer
$ g^{-1}(x)=\frac{6x+7}{12}$
Work Step by Step
We are given the function, $g(x)=\frac{12x-7}{6}$. First, we must replace $g(x)$ with y.
$y=\frac{12x-7}{6}$
Next, interchange x and y.
$x=\frac{12y-7}{6}$
Next, multiply both sides by 6.
$6x=12y-7$
Add 7 to both sides.
$12y=6x+7$
Divide both sides by 12.
$y=\frac{6x+7}{12}$
Finally, replace y with $g^{-1}(x)$.
$ g^{-1}(x)=\frac{6x+7}{12}$
