Question

Question #294f3

Answer 1

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

Explanation:

So, you're given `f(x) = x/(x+1)`. To find the inverse, or `f^-1(x)`, there are 2 steps:

1. "Replace the `x` and `y` (or `f(x)`) variables"
2. Solve for `y` in terms of `x`

So, first we replace and get `x=y/(y+1)`.

Now, the best strategy to solve for `y` is to follow these steps:
1. multiply out all of the denominators with variables to bring them into the numerator
2. move all of the terms with the variable you're looking for (`y`) to one side
3. Factor out that variable
4. Divide to isolate the variable

Step `1`:
`(y+1)*x = y/(y+1)(y+1)`

`x*y+x = y`

Step `2`:
`x*y-y=-x`

Step `3`:
`y(x-1) = -x`

Step `4`:
`y = -x/(x-1)`