Results 1 to 3 of 3

Math Help - Determine points of continuity

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Determine points of continuity

    Define f:\mathbb{R}\to\mathbb{R} as follows:
    f(x)=\begin{cases}x-\left\lfloor x\right\rfloor, & \text{if} \ \left\lfloor x\right\rfloor \text{is even}\\x-\left\lfloor x+1\right\rfloor, & \text{if} \ \left\lfloor x+1\right\rfloor \ \text{is odd}\end{cases}
    Determine the points where f(x) is continuous.

    I graphed the function and obtain y=x, \ [0,1) \ \text{and} \ y=x-1, \ [0,1).
    Nothing in the interval (1,2) and the same lines shifted to the right 2 units and this repeats in both directions.
    Therefore, the function is discontinuous everywhere. How can I prove this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1

    Re: Determine points of continuity

    Quote Originally Posted by dwsmith View Post
    Define f:\mathbb{R}\to\mathbb{R} as follows:
    f(x)=\begin{cases}x-\left\lfloor x\right\rfloor, & \text{if} \ \left\lfloor x\right\rfloor \text{is even}\\x-\left\lfloor x+1\right\rfloor, & \text{if} \ \left\lfloor x+1\right\rfloor \ \text{is odd}\end{cases}
    Determine the points where f(x) is continuous.
    Note that \left\lfloor 2 \right\rfloor\text{ is even and }\left\lfloor 2+1 \right\rfloor\text{ is odd}
    Thus f(2) has two values.

    So this function is ill-defined.

    Please Edit and Correct.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Re: Determine points of continuity

    Quote Originally Posted by Plato View Post
    Note that \left\lfloor 2 \right\rfloor\text{ is even and }\left\lfloor 2+1 \right\rfloor\text{ is odd}
    Thus f(2) has two values.

    So this function is ill-defined.

    Please Edit and Correct.
    I solved so correcting the mistake is not needed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to Determine a Hyperbola From Points
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: March 6th 2011, 03:07 AM
  2. determine coplanar points
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 25th 2010, 03:00 AM
  3. Determine the Points
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 14th 2009, 12:42 PM
  4. Determine the coordinates of the points.
    Posted in the Geometry Forum
    Replies: 1
    Last Post: August 31st 2009, 11:32 PM
  5. determine angle of 3 points
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 22nd 2009, 09:48 PM

/mathhelpforum @mathhelpforum