# Math Help - inverse function

1. ## inverse function

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

2. Originally Posted by golden330ci
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
You need to solve $x = y^3 + 36y^2 + 432 y = (y + 12)^3 - 12^3$ for y:

$x + 12^3 = (y + 12)^3 \Rightarrow .......$

3. Originally Posted by mr fantastic
You need to solve $x = y^3 + 36y^2 + 432 y = (y + 12)^3 - 12^3$ for y:

$x + 12^3 = (y + 12)^3 \Rightarrow .......$
In response to the pm
Originally Posted by golden330ci
i worked the problem through but still came up with an incorrect solution, can you help me out a bit?....why the (y+12)^3? inverse are my weakeness...
$y = x^3 + 36x^2 + 432x$.

This is exactly the same as $y = (x + 12)^3 - 12^3$.

To find the inverse function you swap x and y around: $x = (y + 12)^3 - 12^3$

and solve for y: $y = (x + 12^3)^{1/3} - 12 = (x + 1728)^{1/3} - 12 = \sqrt[3]{x + 1728} - 12$.

This is the inverse function.

4. i understand how to work the problem after y=(x+12)^3-12^3...but how/why is that the same as the original equation?

5. Originally Posted by golden330ci
i understand how to work the problem after y=(x+12)^3-12^3...but how/why is that the same as the original equation?
it is just a pattern you have to notice.

$(x + a)^3 = x^3 + 3ax^2 + 3a^2x + a^3$ .............(by using the binomial theorem, Pascal's triangle, or simply the distributive law)

here, your $a$ is 12. So that $(y + 12)^3 = y^3 + 3(12)y^2 + 3(12^2)y + 12^3 = ~{\color{red} y^3 + 36y^2 + 432y}~ + 12^3$. What is in red is exactly what we started with. Since there was no $12^3$ term in the original form, he had to subtract it, hence the $-12^3$ part