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Confusion with Inverse Functions AP Calc

  1. Nov 11, 2009 #1
    1. The problem statement, all variables and given/known data
    1) Given f(x)= .01x³ + .7x -2 . Approximate ƒ−1(3).

    2)Given f(x) = (x³) / (x²+1) and g(x) = ƒ–1(x). Evaluate g'(2)



    3. The attempt at a solution

    1) Would this be correct? 3=.01x^3 + .7x -2
    But then, how would I find x at 3?


    2) I am confused about going about solving this problem. Any help would be appreciated@!!

    Thanks
     
  2. jcsd
  3. Nov 11, 2009 #2
  4. Nov 11, 2009 #3
    OK, so for number one, I wouldn't just set the function equal to 3 and then solve?? And if I would do that how would I find x??
     
  5. Nov 11, 2009 #4

    Mark44

    Staff: Mentor

    For #1, you're looking for a number x0 such that f(x0) [itex]\approx[/itex] 3. Equivalently, x0 [itex]\approx[/itex] f-1(3)
     
  6. Nov 11, 2009 #5
    So then I have 3=.01x^3 + .7x -2. What step would I take to solve this problem next?
     
  7. Nov 11, 2009 #6

    Mark44

    Staff: Mentor

    How about adding 2 to both sides? This will give you .01x^2 + .7x = 5. At that point I would pick a value and put it in for x on the left side and see how close I got to 5. If the result is larger than 5, pick a smaller value and repeat the process so that you get closer and closer to 5 as the result.
     
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