1. Supply function firm

Hello, I wasn't sure where to put this so I hope it is alright. My problem is the following: I need to determine the supply function of a firm which has the cost function C(y)= 3y^3-6y^2+4y. I know the MC(y) = 9y^2-12y+4 Normally I would solve MC = P and use the ABC formula on 9y^2-12y+(4-p) but I keep getting the wrong answer. I do have a solution manual(the solution is apparently is y(p) = (2/3)+(1/3*sqrt(p)) but it uses the inverse of the MC function but I have no idea why that is being used and how to calculate said inverse because I normally only use the former method and the manual gives no calculations whatsoever. I hope this is clear enough and that someone can help me clear this up. Barbor

2. No clue what the context is or what the ABC formula does but sounds like you want y asthe subject of:

9y^2-12y+4 = p

$\displaystyle (3y-2)^2 = p$
$\displaystyle 3y-2=\pm p$
$\displaystyle y=\frac{\pm p+2}{3}$

Assuming there's some reason from context that explains why -p isn't allowed; I'll leave that to you.