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Homework Help: Inverse shminverse

  1. Feb 18, 2010 #1
    1. The problem statement, all variables and given/known data

    If f(x)= x^3 +4x + 6,

    a.) show f(x) is one to one.

    b) Find inverse f(10)... f^-1(10) (hard to write type on a computer)

    c) Find f^-1(10)'


    2. Relevant equations

    f^-1(x)' = 1/[f'(x)*f^-1(10)]


    3. The attempt at a solution

    a.) a function is monotonic when it is either always increasing or always decreasing. You can check by looking at the derivative, f(x)' = 3x^2 + 4. This Function is one to one because it is monotonic (always increasing).

    b.) I simply cannot figure this out. I am pretty sure our professor does NOT want us to try to find a direct equation for f^-1(x). I believe she wants us to use the method she calls "inspection", to look at the problem carefully and figure out a y value, then f^-1(x) = y, so I can find f(10). pretty lost.

    c.) See above... though I know the equation is f^-1(x)' = 1/[f'(x)*f^-1(10)]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 18, 2010 #2

    tiny-tim

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    Hi srfriggen! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    Yes, part a) told you f(x) is increasing, and you can immediately see that f(0) = 6 and f(1) = 11, so f-1(10) must be between 0 and 1 …

    now narrow it down further. :smile:
     
  4. Feb 18, 2010 #3

    That helps a little but doesn't really get to an answer. I have a feeling she meant to write 3x instead of 4x. That would make things a lot more elegant.
     
  5. Feb 18, 2010 #4

    Dick

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    She may also have meant f^(-1)(-10) instead. That would make more sense as well.
     
  6. Feb 18, 2010 #5
    True, -10 would work nicely.

    ok, I've been going batty trying to figure this one out. It was on a small pop quiz last night and she said it shouldn't have taken us more than a minute to do that problem...

    so am I nuts and terrible at calc or does it seem like she made a mistake??? cause I don't see an easy solution to this problem at all.
     
  7. Feb 18, 2010 #6
    What about 0?

    (x-10)^1/2=f^-1(x)

    or am i completely wrong
     
  8. Feb 18, 2010 #7



    The question asks what is f^-1(10). You ask if zero works...

    No, because if f^-1(10)=0, then f(0) would have to equal 10, and f(0) is 0^3+4(0)+6, or 6.
     
  9. Feb 19, 2010 #8
    Thank you all for replying. turns out my teacher did make a mistake. should have been 11, not 10.
     
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