Results 1 to 3 of 3

Thread: Continuity of inverse of a continuous function

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    1

    Continuity of inverse of a continuous function

    I was wondering if someone could help me with a proof:


    Suppose we have the function f such that f is:
    (i) continuous
    (ii) strictly monotonic
    (iii) injective

    Prove the inverse of f is continuous.


    Much appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    (Assuming you have already shown or aren't asked to show that f has an inverse in the first place)

    It will be enough to show that f is open, that is, for any open set U, f(U) is also an open set. In fact, it suffices to consider open intervals. See where you can go from there.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,163
    Thanks
    46
    Quote Originally Posted by georgec5594 View Post
    Suppose we have the function f such that f is:
    (i) continuous
    (ii) strictly monotonic
    (iii) injective

    Hypothesis (iii) is irrelevant. If f is strictly monotonic then, f is injective.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continuity, series, inverse function
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Mar 21st 2010, 02:09 AM
  2. Replies: 8
    Last Post: Mar 27th 2009, 04:23 AM
  3. Continuity - continuous functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 19th 2009, 03:05 AM
  4. Replies: 2
    Last Post: Dec 1st 2007, 02:30 PM
  5. Continuous functions/Limits and continuity
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Aug 31st 2007, 12:40 AM

Search Tags


/mathhelpforum @mathhelpforum