Find the inverse function (find f^-1) f(x)=(x-2)/(3x+3) I have the correct answer, I just don't know how to get to it. answer is: f^(-1) =(-2-3x)/(3x-1)

Question

Find the inverse function (find f^-1)


`f(x)=(x-2)/(3x+3)`

I have the correct answer, I just don't know how to get to it.
answer is:
`f^(-1) =(-2-3x)/(3x-1)`

Answer 1

Explanation:

f(x) = (x-2)/(3x+3). Let y = f(x).

Then y = (x-2)/(3x+3).

y(3x+3) = x - 2

3xy + 3y = x - 2

3xy - x = -3y - 2

x(3y-1) = -(3y+2)

x = -(3y+2)/(3y-1)

Hence, the inverse of f(x) is -(3x+2)/(3x-1).