Results 1 to 7 of 7

Math Help - Range of a multivariable function

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    150

    Range of a multivariable function

    How do you find the range, algebraically, of a multivariable function?

    I'm attempting to prove the following:

    Prove that there do not exist integers m and n such that 12m+15n=1.


    I know there's a different way to do it, but I want to show that 1 is not in the range of the multivariable function f(m,n)=12m+15n.

    I guess I could simply say, "Obviously, 1 is not in the range of this function" but I want to show it algebraically for the proof.

    Any help would be appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by divinelogos View Post
    How do you find the range, algebraically, of a multivariable function?

    I'm attempting to prove the following:

    Prove that there do not exist integers m and n such that 12m+15n=1.


    I know there's a different way to do it, but I want to show that 1 is not in the range of the multivariable function f(m,n)=12m+15n.

    I guess I could simply say, "Obviously, 1 is not in the range of this function" but I want to show it algebraically for the proof.

    Any help would be appreciated!
    Your approach is flawed because 1 is in the range of the function eg. m = 1/12 and n = 0. Your approach does not take into account the simple fact that the 'domain' is required to be the integers not real numbers.

    (This is one reason why I have moved your question to number theory).

    The required proof probably expects you to note that the gcd of 12 and 15 is not 1.
    Last edited by mr fantastic; February 19th 2011 at 11:10 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2010
    Posts
    150
    Quote Originally Posted by mr fantastic View Post
    Your approach is flawed because 1 is in the range of the function. You can't treat it as a multi-variable function because the domain is integers not real numbers.

    (This is one reason why I have moved your question to number theory).

    The required proof probably expects you to note that the gcd of 12 and 15 is not 1.
    Can I simply restrict the domain of the function to integers, and then show that 1 is not in the range?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by divinelogos View Post
    Can I simply restrict the domain of the function to integers, and then show that 1 is not in the range?
    That is exactly what the question has asked you to do!!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2010
    Posts
    150
    Quote Originally Posted by mr fantastic View Post
    That is exactly what the question has asked you to do!!
    Right, but I want to show it algebraically as follows:

    1. If there were integers m and n such that 12m+15n=1, then 1 would be in the range of the function "f(m,n)=1m+15n whose domain is integers"

    2.(this is where I want to show algebraically that 1 is not in the range of that function^^).

    3.Hence, there are not integers m and n such that 12m+15n=1.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by divinelogos View Post
    Right, but I want to show it algebraically as follows:

    1. If there were integers m and n such that 12m+15n=1, then 1 would be in the range of the function "f(m,n)=1m+15n whose domain is integers"

    2.(this is where I want to show algebraically that 1 is not in the range of that function^^).

    3.Hence, there are not integers m and n such that 12m+15n=1.


    What's the problem with simply saying "as 3 divides both of 12 and 15 it divides 12m + 15n , for all

    integers m,n, and ..."??

    Tonio
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2010
    Posts
    150
    Quote Originally Posted by tonio View Post
    What's the problem with simply saying "as 3 divides both of 12 and 15 it divides 12m + 15n , for all

    integers m,n, and ..."??

    Tonio
    There's nothing wrong with it. I just wanted to see how to do it the other way, or if it was even possible
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] How do I graph a multivariable function?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 25th 2010, 04:28 AM
  2. maximum value of a multivariable function ?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 9th 2010, 03:21 AM
  3. Multivariable function fun;
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: October 5th 2009, 09:56 AM
  4. Limit of a Multivariable function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 18th 2008, 11:50 PM
  5. multivariable function- domain and range
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 12th 2008, 04:10 PM

Search Tags


/mathhelpforum @mathhelpforum