How do you find the inverse function of f(x) = x/(x+1)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Find the inverse of the function `f(x) = x/(x+1)`

First, we let `y = f(x).`

So we now can say:  `y = x/(x+1)`

To find the inverse I can switch x and y and solve for y:

First,  `x = y/(y+1)`

Rewrite as:  `x = 1 - (1/(y+1))`

Subtract 1:  `(x - 1) = - 1/(y + 1)`

Multiply by (y + 1):  `(y + 1)(x - 1) = -1`

`yx - y + x - 1 = -1`

`y(x - 1) = -x` Divide by (x - 1)

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

Therefore inverse is: `f^(-1)(x) = - x/(x - 1)`

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial