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

1 Answer
Nov 22, 2015

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

f^(-1)(y) = (8y)/(1-y)f1(y)=8y1y

Explanation:

y = f(x) = x/(x+8) = (x+8-8)/(x+8) = 1-8/(x+8)y=f(x)=xx+8=x+88x+8=18x+8

Hence (adding 8/(x+8)-y8x+8y to both ends):

8/(x+8) = 1 - y8x+8=1y

Hence (multiplying both sides by (x+8)/(1-y)x+81y):

x+8 = 8/(1-y)x+8=81y

So:

x = 8/(1-y) - 8 = 8/(1-y) - (8-8y)/(1-y) = (8y)/(1-y)x=81y8=81y88y1y=8y1y

So:

f^(-1)(y) = (8y)/(1-y)f1(y)=8y1y