How do you find the inverse of f(x) = x / (x + 8)f(x)=xx+8?
1 Answer
Nov 22, 2015
Let
f^(-1)(y) = (8y)/(1-y)f−1(y)=8y1−y
Explanation:
y = f(x) = x/(x+8) = (x+8-8)/(x+8) = 1-8/(x+8)y=f(x)=xx+8=x+8−8x+8=1−8x+8
Hence (adding
8/(x+8) = 1 - y8x+8=1−y
Hence (multiplying both sides by
x+8 = 8/(1-y)x+8=81−y
So:
x = 8/(1-y) - 8 = 8/(1-y) - (8-8y)/(1-y) = (8y)/(1-y)x=81−y−8=81−y−8−8y1−y=8y1−y
So:
f^(-1)(y) = (8y)/(1-y)f−1(y)=8y1−y