x-2/3x+1,determine the inverse.

To determine the inverse of the function, we need to solve for y. Let's continue solving the equation:

3xy + x = y - 2

First, let's move all the terms involving y to one side of the equation:

3xy - y = -x - 2

Next, factor out the common y term:

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

Finally, divide both sides of the equation by (3x - 1) to isolate y:

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

Therefore, the inverse of the function is:

f^-1(x) = (-x - 2)/(3x - 1)