What is the inverse of y = ln(x) + ln(x-6) ?

1 Answer
Jun 8, 2018

For the inverse to be a function a domain restriction will be required:

y'=3+-sqrt(e^x + 9)

Explanation:

y = ln(x) + ln(x-6)

x = ln(y) + ln(y-6)

Apply rule: ln(a) + ln(b) = ln(ab)

x = ln(y(y-6))

e^x = e^(ln(y(y-6)))

e^x = y(y-6)

e^x = y^2-6y

complete the square:

e^x + 9 = y^2-6y +9

e^x + 9 = (y-3)^2

y-3=+-sqrt(e^x + 9)

y=3+-sqrt(e^x + 9)