1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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 of f(x) = x + [x]

  1. Dec 11, 2008 #1
    I'm having trouble finding the inverse of f(x) = x + [x]. I think it comes back to what is the inverse of the greatest integer function, [x]. I have graphed [x], and its inverse is the reflection along the y = x line, which appears to be similar, although the inverse graph is "vertical". Is there a name for this inverse graph? I have tried 1/[x], and [1/x], but those are not it. Also, I can't solve for the inverse by factoring out x.

    If it isn't already too much, I can't seem to find the inverse of f(x) = x/(1-x^2)
    for -1 <= x <=1 either, since I can't factor out the x. I have checked that this function is one-to-one on the interval, so it should be possible. Are there any suggestions?

    Thanks in advance!
  2. jcsd
  3. Dec 11, 2008 #2
    There is no inverse to x --> [x] due to its not being injective.
  4. Dec 11, 2008 #3

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    The problem is the holes in the range of [itex]f:\mathbb R \to \mathbb R[/itex] with [itex]f:x\to x + \lceil x \rceil[/tex]. For example, there is no real x that yields f(x)=1.5.

    That said,

    y-\frac{\lfloor y \rfloor}2

    but only if [itex]\lfloor y \rfloor[/itex] is even. The inverse function is undefined if [itex]\lfloor y \rfloor[/itex] is odd.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Inverse Date
Inverse trig functions Feb 16, 2018
Inverses in Z/mZ* Jan 31, 2018
Inverse Z transform problem Nov 20, 2017
The adjoint of the inverse Oct 22, 2017
PDF to CDF and Inverse CDF Oct 22, 2017