Results 1 to 3 of 3

Math Help - Domain and range

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    7

    Domain and range

    Hi,
    I am stuck with finding the domain and range of g(x)=\frac{x}{x-1}. I think that the domain is all values except x=1. But what about the range?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hi there.

    Quote Originally Posted by toprun91 View Post
    Hi,
    I am stuck with finding the domain and range of g(x)=\frac{x}{x-1}. I think that the domain is all values except x=1.
    That's true,

    It is okay to write
     D = \mathbb{R} \backslash \{1\}

    Quote Originally Posted by toprun91 View Post
    But what about the range?

    I suggest range(g) = \mathbb{R}

    But I am not sure about it, because a long polynomial division leads to

    a(x) = 1 + \frac{1}{x-1}

    So a(x) is a horizontal asymptote, a(x) tends to +1, if x \to \pm \infty

    So the range could be range(g) = \mathbb{R} \backslash \{1 \} as well
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,417
    Thanks
    1329
    Another way to find range is to "reverse" the fraction- solve for x- so that domain and range are swapped.

    If y= \frac{x}{x-1} then [tex]y(x-1)= xy- y= x. Then xy- x= y so x(y- 1)= y. The fraction inverts into x= \frac{y}{y- 1}. Now we can see that y can be any number except 1 so that the range of the original fraction is, indeed, R\{1}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: September 16th 2009, 06:25 AM
  2. Domain and Range of f(x,y)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 1st 2008, 09:20 PM
  3. domain and range
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 30th 2008, 02:54 AM
  4. Range and Domain
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: September 28th 2008, 04:42 PM
  5. domain and range
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: July 17th 2007, 01:34 PM

Search Tags


/mathhelpforum @mathhelpforum