Question

If f(x)= x/x-1 what is f^-1(x)

Answer 1

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

Explanation:

our function is

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

we are asked to determine the inverse of the above function . In order to do so we put f(x) = y and separate x in terms of y and in the final answer , we replace x with y and x with h(x)

let us see how do we do that

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

multiplying both sides by (x-1)

`y(x-1)=x`

`xy-y=x`

subtracting x from both sides and adding y on both sides

`xy-x=y`

`x(y-1)=y`

dividing both sides by (y-1)

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

we now replace x with y and x with
`f^(-1)(x)`

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