as you should already know, to get the inverse of any relation we start off by doing a quick switcheroo on the variables and then solve for "y".
[tex]\stackrel{f(x)}{y}=\cfrac{3}{4}x+9\implies \stackrel{quick~switcheroo}{x=\cfrac{3}{4}y+9}\implies x-9=\cfrac{3y}{4}\implies 4x-36=3y \\\\\\ \cfrac{4x-36}{3}=y\implies \cfrac{4}{3}x-12=\stackrel{f^{-1}(x)}{y}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
