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!

Discrete functions

  1. Apr 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose A, B, C are sets and [URL]http://latex.codecogs.com/gif.latex?f:A\to%20B,%20\text{%20and,%20}%20g:B\to%20C[/URL]

    If f and g are one-to-one so is [PLAIN]http://latex.codecogs.com/gif.latex?g\circ%20f [Broken] [Broken].[/URL]

    If f and g are onto, so is [URL]http://latex.codecogs.com/gif.latex?g\circ%20f[/URL]


    2. Relevant equations

    One-to-one: [URL]http://latex.codecogs.com/gif.latex?(x,b),(y,b)\epsilon%20f%20\text{%20we%20must%20have%20}%20x=y[/URL]

    Onto: Let [URL]http://latex.codecogs.com/gif.latex?f:A\to%20B,[/URL] we say f is onto B provided for every [URL]http://latex.codecogs.com/gif.latex?b\epsilon%20B[/URL] there is an [URL]http://latex.codecogs.com/gif.latex?a\epsilon%20A[/URL] so that [URL]http://latex.codecogs.com/gif.latex?f(a)=b[/URL]

    3. The attempt at a solution

    So.. I'm sort of lost, I've had this problem in the past, and did not understand it at all, and now its come back to haunt me. I know that:

    [URL]http://latex.codecogs.com/gif.latex?im%20f%20=%20B[/URL]
    [URL]http://latex.codecogs.com/gif.latex?dom%20f%20=%20A[/URL]
    [URL]http://latex.codecogs.com/gif.latex?im%20g%20=%20C[/URL]
    [URL]http://latex.codecogs.com/gif.latex?dom%20g%20=%20B[/URL]

    But from there I'm sort of lost. Help would be much appreciated!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 8, 2010 #2
    Start with g(f(x))=g(f(y)), and show x=y.
     
  4. Apr 8, 2010 #3
    Call fx=a, fy=b , since g is one to one, what can you can about g(a)=g(b)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Discrete functions
Loading...