Results 1 to 3 of 3

Thread: Injective functions

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    81

    Exclamation Injective functions

    Let f : A → B et g : B → C be 2 functions

    Show that if g ◦ f is injective, then f has to be injective
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Focus's Avatar
    Joined
    Aug 2009
    Posts
    228
    This isn't true, take $\displaystyle \cdot ^2:\mathbb{R}\rightarrow[0,\infty)$ and $\displaystyle \sqrt{}:[0,\infty)\rightarrow [0,\infty)$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Apr 2009
    From
    Mxico
    Posts
    721
    Quote Originally Posted by Focus View Post
    This isn't true, take $\displaystyle \cdot ^2:\mathbb{R}\rightarrow[0,\infty)$ and $\displaystyle \sqrt{}:[0,\infty)\rightarrow [0,\infty)$.
    Notice that $\displaystyle \sqrt{} \circ \cdot^2$ is not injective.

    As for the problem assume $\displaystyle f(x)=f(y)$ then $\displaystyle g(f(x))=g(f(y)) $which implies $\displaystyle x=y$ by the injectivity of $\displaystyle g\circ f$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Properties of injective functions
    Posted in the Calculus Forum
    Replies: 18
    Last Post: Jun 8th 2010, 05:02 PM
  2. injective functions
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: Nov 21st 2009, 11:34 AM
  3. Replies: 1
    Last Post: Sep 21st 2009, 08:01 PM
  4. injective functions
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: May 31st 2008, 09:32 AM
  5. Injective Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 24th 2007, 12:53 AM

Search Tags


/mathhelpforum @mathhelpforum