Question

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

Answer 1

`y = xy - x`

Explanation:

To find the inverse of a function, we swap the `x` to a `y` and vice versa.

Therefore, the equation becomes:
`x = y/(y-1)`

Now, like the normal way to write equations, we want what `y` equals.

So Let's make `y` alone by multiplying both sides by `color(blue)(y-1)`:
`x quadcolor(blue)(*quad(y-1)) = y/(y-1) quadcolor(blue)(*quad(y-1))`

`x(y-1) = y`

Distribute:
`xy - x = y`

Write with `y` on the left hand side:
`y = xy - x`

Hope this helps!