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!

Proving the graph of a composite function

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f : A → B, g : B → C be functions where A,B,C are sets. ConsiderΓf ⊂A×B,the graph of f,Γg ⊂B×C,the graph of g. Now consider the sets Γ f ×C ⊂ A×B×C and A×Γg ⊂A×B×C. LetΓ=θ(Γf ×C∩A×Γg)⊂A×C where θ : A×B×C → A×C is the projection defined as θ((a,b,c))=(a,c). Show that Γ is the graph of g◦f.
    2. Relevant equations



    3. The attempt at a solution

    I think that I should find a way to show that the first projection of gamma is a bijection. But i dont know how I can do that.
     
  2. jcsd
  3. Oct 23, 2011 #2
    please help ive been trying for so long
     
  4. Oct 24, 2011 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Then show us what you have been doing all that time!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proving the graph of a composite function
  1. Functions composition (Replies: 2)

Loading...