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How to rank random function from smallest to largest with inverse f included?

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data

    The graph of y=f(x) is shown below.

    http://newton.science.sfu.ca/cgi-bin/plot.png?file=public_public_1346904771_18810161_plot.data [Broken]
    Rank the following from smallest(1) to largest(4).

    f−1(0)
    f(0)
    f(5)
    f−1(5)

    2. Relevant equations

    none available

    3. The attempt at a solution

    f−1(0) 1
    f(0) 3
    f(5) 2
    f−1(5) 4


    Because if f(0) is 4, wouldn't that make the co-ordinates (0,4) so inverse would be (4, 0) so inverse f(0) would be 0 no? But I know this is wrong. I don't what I am doing wrong.
    Please help
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Sep 6, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Knowing that f(0)= 4 tells you that [itex]f^{-1}(4)= 0[/itex], not [itex]f ^{-1}(0)[/itex]. What you need is some x such that f(x)= 0. Where is f(x)= 0 on your graph?
     
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