1. Limited time only! Sign up for a free 30min personal 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!

Dual-output Function?

  1. Nov 23, 2008 #1
    "Dual-output" Function?

    This isn't homework: I am experimenting with factorization.

    Does anyone know of a function f(x) which for some value of x returns one value for f(x), but for every other value of x returns some other value?

    Example: I'm trying to find a function f(x), where

    x = 0, f(x) = 1
    x != 0, f(x) = 0

    My function is only dealing with non-negative integers, if that helps.

    I've already derived a function that does this, but it uses absolute values, which is a nuisance.

    Anyone know of anything like this?

    For reference, here is my formula:

    [tex]f(x) =\frac{1-\frac{\left|2x-1\right|}{2x-1}}{2} = \frac{\left|4x-2\right| - 4x-2}{8x-4}[/tex]
     
    Last edited: Nov 23, 2008
  2. jcsd
  3. Nov 23, 2008 #2

    Vid

    User Avatar

  4. Nov 23, 2008 #3

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    Re: "Dual-output" Function?

    That's the characteristic function of zero (Sloane's http://www.research.att.com/~njas/sequences/A000007 [Broken]). But your post seemed to focus on giving it a closed form. Why?
     
    Last edited by a moderator: May 3, 2017
  5. Nov 24, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: "Dual-output" Function?

    What exactly do you want? When you say "f(0)= 1, f(x)= 0 if x is not 0" you have already defined a function. And if you want a closed form, why is absolute value a "nuisance"?
     
  6. Nov 24, 2008 #5
    Re: "Dual-output" Function?

    Thanks to those who have responded, you've helped a lot.

    @Vid: The link you supplied helped me solve another problme I was working with, so thanks.

    @CRGreathouse: That, too, is of great help. I wasn't sure if 0^0 would be considered defined, but that greatly simplifies my procedure.

    @HallsofIvy: Yes, that techincally defines a function, but I was looking for a mathematical equation which would supply that result. Two ways are the one I supplies in ym OP, and f(x) = 0^x.

    Also, I called absolute value a nuisance because I am build an equation and I need to then invert it. If there are absolute values, then things get very tricky, by which I mean impossible to solve.
     
  7. Nov 24, 2008 #6

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Re: "Dual-output" Function?

    It's interesting you decided f(x)=0^x is an equation that gives this, since 0^x has to be defined at x=0 separately anyway, so you haven't really gained anything. And there's no way in hell you're going to invert this sucker
     
  8. Nov 24, 2008 #7

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    Re: "Dual-output" Function?

    This function (regardless of whether you view it as a closed-form equation or not) can't be inverted. f(9) = f(3) = 0, so what would f^-1(0) be?
     
  9. Nov 24, 2008 #8
    Re: "Dual-output" Function?

    Terribly sorry, I misspoke/posted. By "invert," I meant not the function, but the final equation that I'm working on.
     
  10. Nov 25, 2008 #9

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    Re: "Dual-output" Function?

    Yes, but inverting the final equation will involve inverting that special function.
     
  11. Nov 25, 2008 #10

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    Re: "Dual-output" Function?

    Actually, I've decided that using the characteristic function of 0 essentially allows you to build piecewise functions, so perhaps you can simply invert piecewise.
     
  12. Nov 25, 2008 #11

    Ben Niehoff

    User Avatar
    Science Advisor
    Gold Member

    Re: "Dual-output" Function?

    If your function only needs to be defined over the integers, you can try

    [tex]f(n) = \frac{\sin \pi n}{n}[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook