Question

Find the inverse of f(x)=(x+1)(x+2). Show your work how to get the answer.

Answer 1

`f^(-1)(x)=(1-2x)/(x-1)`

Explanation:

1. replace f(x) with x, and x with y:
`f(x)=(x+1)/(x+2) == > x=(y+1)/(y+2)`

2. Solve for y:

`x=(y+1)/(y+2)`

`x(y+2)=y+1`

`xy+2x=y+1`

`xy-y=1-2x`

`y(x-1)=1-2x`

`y=(1-2x)/(x-1)`

3. Replace y with f⁻¹(x)