Results 1 to 6 of 6

Math Help - Range of function

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    171

    Range of function

    Hi

    What will be the range of the function f(x) = 1-1/x .

    1. The domain is given as [0, infinity)

    2. The domain is given as [0, infinity]

    I am primarily confused if "1" will be included or not? The limit of the function tends to 1 but it will never actually reach 1. So, will the range be [-infinity,1) or [-infinity,1] or (-infinity,1) or (-infinity,1]

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,402
    Thanks
    1273
    Quote Originally Posted by champrock View Post
    Hi

    What will be the range of the function f(x) = 1-1/x .

    1. The domain is given as [0, infinity)

    2. The domain is given as [0, infinity]

    I am primarily confused if "1" will be included or not? The limit of the function tends to 1 but it will never actually reach 1. So, will the range be [-infinity,1) or [-infinity,1] or (-infinity,1) or (-infinity,1]

    thanks
    Hint: Find the range of the function f(x) = \frac{1}{x} in the domain x \geq 0.

    The multiplication by -1 gives a reflection in the x-axis, and the addition of 1 is a translation of 1 unit vertically upward.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    I write the answer but when I see the member above me give you a hint I edit it

    note you can't write the interval closed from the direction of infinity
    like this

    (0,infinity]

    the correct like this

    (0,infinity)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2008
    Posts
    171
    Quote Originally Posted by Amer View Post
    I write the answer but when I see the member above me give you a hint I edit it

    note you can't write the interval closed from the direction of infinity
    like this

    (0,infinity]

    the correct like this

    (0,infinity)
    hmm ok . (0,infinity) is because infinity cant be included in the set right? Its not any proper number.

    @Prove It : I found the range. Its coming out to be -infinity to 1. But I am not sure if 1 is actually included or not because
    Lim 1/x (x tends to infinity) ---> 0
    so 1-1/x = 1-0 = 1
    but
    But 1/(some very large number ) ----> some very tiny number like 0.000000000045
    So, 1-1/x = 1-some very tiny number. = 0.99999999999999434

    SO, the range is (-infinity,1) or (-infinity,1] ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    the first one (-infinity,1)

    thanks to prove it
    Last edited by Amer; June 6th 2009 at 04:43 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,402
    Thanks
    1273
    Quote Originally Posted by champrock View Post
    hmm ok . (0,infinity) is because infinity cant be included in the set right? Its not any proper number.

    @Prove It : I found the range. Its coming out to be -infinity to 1. But I am not sure if 1 is actually included or not because
    Lim 1/x (x tends to infinity) ---> 0
    so 1-1/x = 1-0 = 1
    but
    But 1/(some very large number ) ----> some very tiny number like 0.000000000045
    So, 1-1/x = 1-some very tiny number. = 0.99999999999999434

    SO, the range is (-infinity,1) or (-infinity,1] ?
    Let's put it this way...

    In the domain x > 0, (since x \neq 0 as pointed out earlier), the range of the function \frac{1}{x} is y > 0, or in interval notation, (0, \infty).

    Notice that as x \to \infty, y \to 0. BUT since we can never reach \infty, y will never reach 0.

    Now the reflection in the x axis means that the range of -\frac{1}{x} becomes y < 0, or to use interval notation, (-\infty, 0).

    The translation of 1 unit vertically upward means that the range of 1 - \frac{1}{x} is y < 1, or (-\infty, 1) in interval notation.


    So to answer your question, you do NOT include the 1 in the range.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. range of the function
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 30th 2010, 06:19 AM
  2. The range of this function?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 17th 2010, 12:42 PM
  3. Range of a function?
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: December 18th 2009, 01:00 PM
  4. Function Range.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 28th 2009, 07:26 PM
  5. range of function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 18th 2009, 12:45 PM

Search Tags


/mathhelpforum @mathhelpforum