Results 1 to 3 of 3

Thread: multivariable function- domain and range

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    22

    multivariable function- domain and range

    $\displaystyle f(x, y)=\sqrt{(4-x^2-y2)}$

    domain 4x-x^2-y^2 has to be > or equal to 0, so x^2+y^2 < or equal to 4.

    range: I have no idea how to find the range here.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Quote Originally Posted by dataspot View Post
    x^2+y^2 < or equal to 4
    Domain:

    Well, yes, but what is that? Do you see the border of this region as a circle? The region contained within the circle is a ...?

    Range:

    What happens for x = y = 0? Is that significant?
    What do you know about the "Principle" square root? Positive? Negative? Zero?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by dataspot View Post
    $\displaystyle f(x, y)=\sqrt{(4-x^2-y2)}$

    domain 4x-x^2-y^2 has to be > or equal to 0, so x^2+y^2 < or equal to 4.

    range: I have no idea how to find the range here.
    Yes you are right, the range is the interior and edge of the circle of radius of two centered at $\displaystyle (0,0)$

    For the range think the max and min of $\displaystyle f(x,y)=\sqrt{4-(x^2+y^2)}$ bounded by $\displaystyle x^2+y^2\leq{4}$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Range of a multivariable function
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: Feb 20th 2011, 03:19 PM
  2. Domain of a multivariable function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 5th 2010, 06:49 AM
  3. Domain of a multivariable function
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Nov 5th 2009, 07:46 PM
  4. What is the domain and range of this function?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 22nd 2009, 12:13 PM
  5. Replies: 1
    Last Post: Nov 10th 2008, 08:27 PM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum