Question

How do you find the inverse of `f(x) = (1-2x) / (1+x)`?

Answer 1

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

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

`implies y(1+x)=1-2x implies y+xy=1-2x implies 2x+xy=1-y`
`implies x(2+y)=1-y implies x=(1-y)/(2+y)`
Now interchange `x` and `y`
`implies y=(1-x)/(2+x)`
`implies f^-1(x)=(1-x)/(2+x)`