Question #294f3

1 Answer
Feb 10, 2017

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)