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Inverse function

  1. Feb 3, 2008 #1
    Hi i'm trying to remember inverse functions for calculus but i'm having a few problems. So any help would be appreciated.

    f(x)= 2x^3 + 3x^2 + 7x+ 4

    So I have no clue how to solve this for the inverse. I know how to do basic ones. But i've forgotten these kind. So can i just get a step in the right direction.
     
  2. jcsd
  3. Feb 3, 2008 #2

    Dick

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    You can get an inverse expression for a general cubic only by using the cubic formula. I DON'T recommend this. It's too complicated. What's the actual problem you need to solve? You probably don't need an explicit formula.
     
  4. Feb 3, 2008 #3
    I'd agree, it would depend on the problem. You could use the cubic formula, but its pretty nasty.
     
  5. Feb 4, 2008 #4
    Well I was hoping their was a nice way of doing b/c I knew about the cubic formula but wasn't about to use it for this. The actual question though was to find (f^-1)'(a) and the a= 4. I thought I had to find the inverse of the f(x) to solve the problem. Is there another way?
     
  6. Feb 4, 2008 #5

    Dick

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    Yes there is. f^(-1)(f(x))=x. Differentiate both sides and use the chain rule. f^(-1)'(f(x))*f'(x)=1. So f^(-1)'(f(x))=1/f'(x). If you want to use this at f(x)=a=4, You still have to find a value of x such that f(x)=4. But that's a lot easier problem than finding the general inverse.
     
  7. Feb 4, 2008 #6
    Oh, okay I see what your saying I didn't think about using f(x)=a=4. Thank you
     
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