Swap out your x and y
Now, divide so you can solve for y easier:
Now, continue?.
so you want to solve for
.........multiplied both sides by
..........expanded the brackets on the left
..........added on both sides
.........factored out from the left hand side
and that's your inverse function
EDIT: Ah, I didn't see that you responded, galactus. But i'll leave what i did up since i used a different method