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Math Help - inverse function

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by golden330ci View Post
    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 .......
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    Quote Originally Posted by mr fantastic View Post
    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
    Quote 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.
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    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?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by golden330ci View Post
    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
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