Question #294f3

1 Answer
Feb 10, 2017

y=(-x)/(x-1)y=xx1

Explanation:

So, you're given f(x) = x/(x+1)f(x)=xx+1. To find the inverse, or f^-1(x)f1(x), there are 2 steps:

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

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

Now, the best strategy to solve for yy 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 (yy) to one side
3. Factor out that variable
4. Divide to isolate the variable

Step 11:
(y+1)*x = y/(y+1)(y+1)(y+1)x=yy+1(y+1)

x*y+x = yxy+x=y

Step 22:
x*y-y=-xxyy=x

Step 33:
y(x-1) = -xy(x1)=x

Step 44:
y = -x/(x-1)y=xx1