Find the inverse of the function y = x^2 + 12x

y=x\\

x=y^{2} + 12y\\

y^{2} + 12y -x = 0\\

Delta = (12^{2}) - 4.1.(-x) = 144 +4X = 36.(4+x)

\sqrt{Delta} = 6 . \sqrt{(4+x)} \\

y' = \frac{-12 + 6.(\sqrt{(4+x)}}{2} = -6 + 3.\sqrt{(4+x)}\\

y" = -6 - 3.\sqrt{(4+x)}

y' = 3.\sqrt{(4+x)} - 6\\

y''= -3.\sqrt{(4+x)} - 6\\