Given the function [tex] f(x)=\frac{6x+9}{x-7} ,x\neq 7 [/tex].
Let [tex] y=\frac{6x+9}{x-7} [/tex]. Now solve for x,
[tex] y=\frac{6x+9}{x-7} \\
y(x-7)=6x+9\\
yx-6x=9+7y\\
x(y-6)=9+7y\\
x=\frac{9+7y}{y-6}
[/tex]
Thus, the inverse function is
[tex] f^{-1}(x)=\frac{9+7x}{x-6},x\neq 6 [/tex]
