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Homework Help: Find the derivative of the inverse function

  1. Nov 19, 2006 #1
    So I need to find the derivative of the inverse function. I know that f is one-to-one and is continous. Also I know that f'(x)=1+[f(x)]^2. I found the inverse writing my equation like f(x)=x+(1/3)[f(x)]^3 then I switch the variables and get that my inverse function=(1/3)x^3 - x. Then I just take the derivative and end up with x^2 - 1. Is this correct?
  2. jcsd
  3. Nov 19, 2006 #2
    :blushing: First, sorry for my poor english.
    I don't think you are right.Because when you switch the variables in the equation you have to pay attention to the ranges of all variables.You can see in your equation f(x)=x^2-1,the range of x is(-∞,∞),but the range of f(x) is [-1,∞).So what you do is not only switch the variables but also write the range of x at the end of your equation.:tongue2:
    Last edited by a moderator: Nov 19, 2006
  4. Nov 19, 2006 #3
    Hmmm...But isn't the range of f(x) (-infinity, infinity)?
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