Find the inverse of the cubic function What is the resulting equation when $y=x^3 + 2x^2$ is reflected in the line $y=x$ ? 
I have tried and tried and am unable to come up with the answer. 
The furthest I was able to get without making any mistakes or getting confused was $x= y^3 + 2y^2$. What am I supposed to do after that step? 

Given $$ y=x^3+2*x^2 $$ solve for x:
We can use the cubic formula:
for $$0 = a x^3 + b x^2 + c x + f$$
x equals:
$$-\frac{\sqrt[3]{\sqrt{\left(27 a^2 f-27 a^2 y-9 a b c+2 b^3\right)^2+4 \left(3 a
   c-b^2\right)^3}+27 a^2 f-27 a^2 y-9 a b c+2 b^3}}{3 \sqrt[3]{2}
   a}+\frac{\sqrt[3]{2} \left(3 a c-b^2\right)}{3 a \sqrt[3]{\sqrt{\left(27 a^2 f-27
   a^2 y-9 a b c+2 b^3\right)^2+4 \left(3 a c-b^2\right)^3}+27 a^2 f-27 a^2 y-9 a b
   c+2 b^3}}-\frac{b}{3 a}
 $$
This gives us:
$$y(x) = \frac{1}{3} (-(3 \sqrt{3} \, \sqrt{27 x^2-32 x}-27 x+16)^{1/3}/2^{1/3}-(4 2^{1/3})/(3 \sqrt{3} \, \sqrt{27 x^2-32 x}-27 x+16)^{1/3}-2)$$
