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Derivative of an Inverse

  1. Dec 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Assume that the Derivative Rule for Inverses holds. Given that f(x) = x + f(x), and g(t) = f-1(t), which of the following is equivalent to g'(t)?
    a. g'(t) = 1 + t2
    b. g'(t) = 1 + t4
    c. g'(t) = 1 + g(x)
    d. g'(t) = 1 / (1 + t4)
    2. Relevant equations



    3. The attempt at a solution
    This question popped up on my recent calc final and my friends and I cannot agree on what the answer is. I answered with C, and most of my friends answered D, arguing that the fraction makes it correct. Can somebody with more knowledge explain this to me? Thank you!
     
  2. jcsd
  3. Dec 17, 2012 #2

    Dick

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    I don't think any functions satisfy f(x)=x+f(x). Can you correct the statement?
     
  4. Dec 17, 2012 #3
    That was the function given to us on the test as best as I can remember. It might have been something like f(x)= x + f(x)^3, but definitely f(x) = x + f(x)
     
  5. Dec 17, 2012 #4

    Dick

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    f(x)=x+f(x) means f(x)-f(x)=x. So x=0. It can't be an identity for the function f(x). Can you check with your classmates and figure out what the real question is?
     
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