having a problem figuring this one out, i understand basic rules applied to functions to find there inverses but can some one please help me find the inverse of this x^3+36x^2+432x...thanks to all that can help
In response to the pm
$\displaystyle y = x^3 + 36x^2 + 432x$.Originally Posted by golden330ci
This is exactly the same as $\displaystyle y = (x + 12)^3 - 12^3$.
To find the inverse function you swap x and y around: $\displaystyle x = (y + 12)^3 - 12^3$
and solve for y: $\displaystyle y = (x + 12^3)^{1/3} - 12 = (x + 1728)^{1/3} - 12 = \sqrt[3]{x + 1728} - 12$.
This is the inverse function.
it is just a pattern you have to notice.
$\displaystyle (x + a)^3 = x^3 + 3ax^2 + 3a^2x + a^3$ .............(by using the binomial theorem, Pascal's triangle, or simply the distributive law)
here, your $\displaystyle a$ is 12. So that $\displaystyle (y + 12)^3 = y^3 + 3(12)y^2 + 3(12^2)y + 12^3 = ~{\color{red} y^3 + 36y^2 + 432y}~ + 12^3$. What is in red is exactly what we started with. Since there was no $\displaystyle 12^3$ term in the original form, he had to subtract it, hence the $\displaystyle -12^3$ part