Results 1 to 3 of 3

Math Help - Function

  1. #1
    Junior Member
    Joined
    Feb 2011
    Posts
    56

    Function

    Functions f and g are defined by

    f(x)= 2x-2, if x<1 and
    f(x)= x^2 -1, if x ≥1

    and g(x) = |x|-x

    Show that the composite function g。f exists for all values of x.

    I have totally no ideas on showing this, can anyone help me?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718
    If f : A -> B and g : B -> C for some sets A, B, C, then the composition g o f : A -> C exists regardless of the particular definitions of f and g. The definition of the composition proves its existence; there is no issue here that requires proving that composition is well-defined.
    Last edited by emakarov; May 24th 2011 at 07:14 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2011
    Posts
    169
    What emakarov said is of course true. Though you could consider the 2 cases.

    When x<1, g(f(x))=g(2x-2)= abs(2x-2)-2x+2 =2-2x-2x+2=4(1-x)

    when x>_1, g(f(x))= g((x^2-1)=abs(x^2-1)+1-x^2=x^2-x^2-1+1=0

    so in both cases the composite function is well defined.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 20
    Last Post: November 27th 2012, 05:28 AM
  2. Replies: 2
    Last Post: April 17th 2012, 10:50 AM
  3. Replies: 0
    Last Post: October 19th 2011, 04:49 AM
  4. Replies: 4
    Last Post: October 27th 2010, 05:41 AM
  5. Replies: 3
    Last Post: September 14th 2010, 02:46 PM

Search Tags


/mathhelpforum @mathhelpforum