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!

An intro to real analysis question. eazy?

  1. Sep 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Let f : A -> B be a bijection. Show that if a function g is such that f(g(x)) = x for
    all x ϵ B and g(f(x)) = x for all x ϵ A, then g = f^-1. Use only the definition of a
    function and the definition of the inverse of a function.

    2. Relevant equations

    3. The attempt at a solution
    well since f is a bijection then there exist an f^-1 that remaps f back to A and since g does that then g is the unique inverse of f, or something like that please help im not very good that this stuff
  2. jcsd
  3. Sep 25, 2010 #2
    Yes, you only need to prove uniqueness of an inverse function. If f(g(x))=x, then g(x) must be the unique argument a for which f(a) = x. And so, this condition completely defines g for all the arguments. g is then obviously equal to f-1.
  4. Sep 25, 2010 #3
    thanks losiu for your response.
    but how do you prove that it is the unique inverse?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - intro real analysis Date
Intro to real analysis Apr 17, 2014
Intro To real analysis problem Apr 23, 2012
Intro to Real Analysis: Supremum Sep 18, 2011
Intro to Real Analysis Sep 15, 2011
A simple Intro to Real Analysis question Oct 1, 2010