1. replace g(x) with y:
[tex]y=\frac{x-1}{x+5}[/tex]2.Replace every x with a y and replace every y with an x
[tex]x=\frac{y-1}{y+5}[/tex]3. Solve for y:
[tex]\begin{gathered} (y+5)x=y-1 \\ yx+5x=y-1 \\ yx-y=-1-5x \\ y(x-1)=-1-5x \\ y=\frac{-1-5x}{x-1} \end{gathered}[/tex]4. Replace y with g−1(x) g− 1 ( x ):
[tex]g(x)^{-1}=\frac{-5x-1}{x-1}[/tex]