The inverse function [tex]f^{-1}(x)[/tex] is such that
[tex]f\left(f^{-1}(x)\right) = x[/tex]
If [tex]f(x)=-\frac34x+9[/tex], then we have
[tex]f\left(f^{-1}(x)\right) = -\dfrac34f^{-1}(x)+9 = x[/tex]
Solve for the inverse :
[tex]-\dfrac34f^{-1}(x)+9 = x \\\\ -\dfrac34f^{-1}(x) = x-9 \\\\ f^{-1}(x) = -\dfrac43(x-9) \\\\ \boxed{f^{-1}(x) = -\dfrac43x+12}[/tex]
