Question

Find an equation for the inverse function

Answer 1

Given the function $f(x)=\frac{6x+9}{x-7} ,x\neq 7$.

Let $y=\frac{6x+9}{x-7}$. Now solve for x,

$y=\frac{6x+9}{x-7} \\ y(x-7)=6x+9\\ yx-6x=9+7y\\ x(y-6)=9+7y\\ x=\frac{9+7y}{y-6}$

Thus, the inverse function is

$f^{-1}(x)=\frac{9+7x}{x-6},x\neq 6$