Results 1 to 4 of 4

Math Help - Injective and surjective

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    5

    Injective and surjective

    Hi everyone,

    I have a math problem i am having a hard time solving. Can someone please help me?

    Show whether or not the function f:R+ -> R+ defined by f(x) = (1/x^2) is

    Injective (one-to-one) or
    Surjective(onto)


    Thank you in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by tironci View Post
    Hi everyone,

    I have a math problem i am having a hard time solving. Can someone please help me?

    Show whether or not the function f:R+ -> R+ defined by f(x) = (1/x^2) is

    Injective (one-to-one) or
    Surjective(onto)


    Thank you in advance
    Say f(x) = f(y) \implies \frac{1}{x^2} = \frac{1}{y^2} \implies x^2 = y^2 \implies x = y \mbox{ since }x,y>0.

    For any y\in \mathbb{R}^+ let x=1/\sqrt{y} then x\in \mathbb{R}^+ and f(x) = y.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    5

    Injective and surjective

    So, it is one-to-one and onto?

    Thank you
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by tironci View Post
    So, it is one-to-one and onto?
    What is the definition of one-to-one? What is the definition of onto? Does the above post prove those things?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Injective, surjective map!
    Posted in the Advanced Algebra Forum
    Replies: 13
    Last Post: December 14th 2010, 12:49 AM
  2. [SOLVED] Injective and Surjective
    Posted in the Calculus Forum
    Replies: 11
    Last Post: September 29th 2010, 02:16 PM
  3. injective and surjective
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 12th 2010, 10:18 AM
  4. Injective if and only if Surjective
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 3rd 2010, 04:37 PM
  5. Injective/Surjective
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 10th 2008, 08:19 AM

Search Tags


/mathhelpforum @mathhelpforum