Results 1 to 4 of 4

Math Help - Continuity of composite function

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    9

    Continuity of composite function

    Is it possible for a composite function f(g(x)) to be continuous at a point 'x=a'
    when g(x) is not continuous at 'x=a'?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,957
    Thanks
    1780
    Awards
    1

    Re: Continuity of composite function

    Quote Originally Posted by deepak View Post
    Is it possible for a composite function f(g(x)) to be continuous at a point 'x=a' when g(x) is not continuous at 'x=a'?
    Let g(x) = \left\{ {\begin{array}{*{20}c}   { - 1,} & {x \leqslant a}  \\   {1,} & {x > a}  \\ \end{array} } \right.\;\& \,f(x) = x^2 .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,396
    Thanks
    1847

    Re: Continuity of composite function

    Or, use f(x)= 1 for all x. That will "smooth" any function!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: Continuity of composite function

    Quote Originally Posted by HallsofIvy View Post
    Or, use f(x)= 1 for all x. That will "smooth" any function!
    If f(x)=1 and g(x)=\frac{1}{x}, f(g(x)) is not continuous at x=0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Composite functions continuity theorem
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 27th 2011, 09:32 AM
  2. continuity of composite function
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: April 21st 2011, 01:41 PM
  3. Composite function
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: April 7th 2011, 10:42 PM
  4. Continuity in Composite functions
    Posted in the Calculus Forum
    Replies: 9
    Last Post: September 5th 2008, 02:44 AM
  5. Composite function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 6th 2008, 03:57 PM

Search Tags


/mathhelpforum @mathhelpforum