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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)