1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Inverse shminverse
  1. Fourier inverse (Replies: 3)

  2. Permutation Inverses (Replies: 60)

  3. Inverse Functions (Replies: 19)

  4. Inverse Jacobian (Replies: 2)

Loading...