Results 1 to 3 of 3

Math Help - create function

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    50

    create function

    can someone help me please build 2 bijection(injective and surjective) functions:
    1. from (0, 1) to (0,infinite )
    2. from (0,1) to [0,infinite)

    thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,793
    Thanks
    1688
    Awards
    1
    Quote Originally Posted by tukilala View Post
    2 bijection(injective and surjective) functions:
    1. from (0, 1) to (0,infinite )
    2. from (0,1) to [0,infinite)
    1. f(x)=\tan \left( \frac{\pi x}{2} \right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member TheAbstractionist's Avatar
    Joined
    Apr 2009
    Posts
    328
    Thanks
    1
    Quote Originally Posted by tukilala View Post
    2. from (0,1) to [0,infinite)
    A bijection 0,\,1)\to[0,\,1)" alt="g0,\,1)\to[0,\,1)" /> is defined by

    g(x)\ =\ \left\{\begin{array}{cl}0 & x=\dfrac12\\[7mm]<br />
\dfrac1{n-1} & x=\dfrac1n,\ n\in\mathbb Z,\ n\ge3\\[7mm]<br />
x & \mbox{otherwise}<br />
\end{array}\right.

    Define F:[0,\,1)\to[0,\,\infty) by F(0)=0 and F(x)=f(x) for 0<x<1 where f is your bijection in (1). Then the required bijection for (2) is F\circ g.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Create a function with certain critical points
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 4th 2011, 10:07 AM
  2. Create a special function
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: November 23rd 2010, 09:15 AM
  3. Replies: 4
    Last Post: September 30th 2010, 05:40 AM
  4. Replies: 1
    Last Post: November 2nd 2008, 06:00 AM
  5. Create function w/ data
    Posted in the Math Software Forum
    Replies: 11
    Last Post: March 3rd 2008, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum