Results 1 to 2 of 2

Thread: continuos function

  1. #1
    Member
    Joined
    Apr 2006
    Posts
    91

    Question continuos function

    suppose f: [a,b] ->R is increasing
    and for every Y in [f(a), f(b)], there is some x0 in [a,b] such that f(x0) = Y

    I want to show that f is a continious function but dont know how to go about this problem , can some one please help ..thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by dopi View Post
    suppose f: [a,b] ->R is increasing
    and for every Y in [f(a), f(b)], there is some x0 in [a,b] such that f(x0) = Y

    I want to show that f is a continious function but dont know how to go about this problem , can some one please help ..thanks
    If $\displaystyle f(x)$ is strictly increasing and maps intervals into intervals. Then $\displaystyle f(x)$ must be continous.

    Use the above fact to prove this partial conversve of the intermediate value theorem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. f(x) differentiable f'(x) not continuos?
    Posted in the Calculus Forum
    Replies: 8
    Last Post: Nov 18th 2010, 05:20 AM
  2. Prove function is Defined & Continuos
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: May 19th 2010, 05:20 AM
  3. Continuos functions in R^n
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Nov 16th 2009, 09:10 AM
  4. Probability Density function of continuos random varaible
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 4th 2009, 11:18 AM
  5. another continuos random variable
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Sep 27th 2006, 11:59 AM

Search Tags


/mathhelpforum @mathhelpforum