## Intermediate Algebra (6th Edition)

$g^{-1}(x)=\frac{6x+7}{12}$
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 $g^{-1}(x)$. $g^{-1}(x)=\frac{6x+7}{12}$