Results 1 to 13 of 13
Like Tree8Thanks
  • 1 Post By MarkFL
  • 1 Post By harpazo
  • 1 Post By DenisB
  • 1 Post By DenisB
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL

Thread: Domain of Rational Functions

  1. #1
    Senior Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    448
    Thanks
    23

    Domain of Rational Functions

    Find the domain of f(x) = (2x)/(x - 2).

    How is this done algebraically?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    2,236
    Thanks
    939

    Re: Domain of Rational Functions

    We see the only restriction that applies in this case is division by zero, so we exclude any values of $\displaystyle x$ which causes the denominator to be zero.
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    448
    Thanks
    23

    Re: Domain of Rational Functions

    Quote Originally Posted by MarkFL View Post
    We see the only restriction that applies in this case is division by zero, so we exclude any values of $\displaystyle x$ which causes the denominator to be zero.
    So, the domain is ALL REAL NUMBERS except that x cannot be 2.
    Thanks from MarkFL
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,070
    Thanks
    413

    Re: Domain of Rational Functions

    Quote Originally Posted by harpazo View Post
    So, the domain is ALL REAL NUMBERS except that x cannot be 2.
    Right. Generally: ........except all cases that create a denominator = 0
    Take a / (b - c): except cases where b - c = 0 or except cases where b = c
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,070
    Thanks
    413

    Re: Domain of Rational Functions

    I find the "division by zero" rule strange: why "not allowed"?

    1 / (2 - 2) = no solution...division by zero...

    1 * (2 - 2)^(-1) = 0

    Get my drift?
    Deb? Mark?
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    2,236
    Thanks
    939

    Re: Domain of Rational Functions

    Your second equation still implies division by zero.
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,070
    Thanks
    413

    Re: Domain of Rational Functions

    Agree...my point is 0 is given as answer by "all or some?" calculators.
    UBasic language does anyhoo...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    2,236
    Thanks
    939

    Re: Domain of Rational Functions

    Quote Originally Posted by DenisB View Post
    Agree...my point is 0 is given as answer by "all or some?" calculators.
    UBasic language does anyhoo...
    W|A returns what they call "complex infinity" for that expression.
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    2,236
    Thanks
    939

    Re: Domain of Rational Functions

    Sweet...the old double post. I don't know what happened, I was flitting from tab to tab.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,070
    Thanks
    413

    Re: Domain of Rational Functions

    Well, was kinda kidding...if I want 0 returned from a division by 0,
    all I need, easy to program...
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    2,236
    Thanks
    939

    Re: Domain of Rational Functions

    Quote Originally Posted by DenisB View Post
    Well, was kinda kidding...if I want 0 returned from a division by 0,
    all I need, easy to program...
    I would likely do something like:

    if (c == 0)
    {
    a = 0;
    }
    else
    {
    a = b/c;
    }
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,070
    Thanks
    413

    Re: Domain of Rational Functions

    n = numerator, d = denominator, r = result

    if d=0 then r=0 else r=n/d

    That's UBasic; whatever yer usin' is too complicated for me
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Senior Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    448
    Thanks
    23

    Re: Domain of Rational Functions

    Interesting notes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Domain for rational function
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: Jan 14th 2018, 03:32 PM
  2. Domain of a rational function
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Aug 27th 2011, 08:42 PM
  3. Replies: 4
    Last Post: Mar 27th 2009, 09:19 PM
  4. Determine the domain of a rational function
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Jun 30th 2008, 05:56 PM
  5. Domain of Rational Functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Jan 31st 2007, 06:35 PM

/mathhelpforum @mathhelpforum