How do you find the inverse of f(x) = x / (x + 8)?

1 Answer
Nov 22, 2015

Let y = f(x) and solve for x to find:

f^(-1)(y) = (8y)/(1-y)

Explanation:

y = f(x) = x/(x+8) = (x+8-8)/(x+8) = 1-8/(x+8)

Hence (adding 8/(x+8)-y to both ends):

8/(x+8) = 1 - y

Hence (multiplying both sides by (x+8)/(1-y)):

x+8 = 8/(1-y)

So:

x = 8/(1-y) - 8 = 8/(1-y) - (8-8y)/(1-y) = (8y)/(1-y)

So:

f^(-1)(y) = (8y)/(1-y)