Question

Find the inverse function of g(x)= x-1÷x+5

Answer 1

`g(x)=(x-1)/(x+5)`

1. replace g(x) with y:

`y=(x-1)/(x+5)`

2.Replace every x with a y and replace every y with an x

`x=(y-1)/(y+5)`

3. Solve for y:

`\begin{gathered} (y+5)x=y-1 \\ yx+5x=y-1 \\ yx-y=-1-5x \\ y(x-1)=-1-5x \\ y=(-1-5x)/(x-1) \end{gathered}`

4. Replace y with g−1(x) g− 1 ( x ):

`g(x)^(-1)=(-5x-1)/(x-1)`