Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By johnsomeone

Math Help - How to make this piecewise continuous (multiple variables, lines)

  1. #1
    Junior Member
    Joined
    Aug 2012
    From
    Maryland
    Posts
    45

    How to make this piecewise continuous (multiple variables, lines)

    f(x) = (x-3)(x-2)(x+1), .....................AND x doesn't equal (equal with the line going across it) -1, 3
    .........____________
    ..........(x+1) (x-3)

    4px-2 ....x=-1

    5mx² - 2x .....x=3


    This is no calculator and the answer isn't as important as knowing the steps to do it. I'm confused as to which number (-1 or 3) I set x equal to before setting the functions equal to eachother.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    147

    Re: How to make this piecewise continuous (multiple variables, lines)

    f(x) = \frac{(x-3)(x-2)(x+1)}{(x+1)(x-3)}, x \notin \{-1, 3 \} already is peicewise continuous. I assume the problem is actually asking how to make it continuous.

    Here are some questions for you. I'm going to define a function on the same domain. Let g(x) = x-2, x \notin \{-1, 3 \}.

    First Question: What's the relationship, if any, between f and g?

    Second Question: Can you think of a continuous function defined on all of \mathbb{R} that equals g on g's domain of ( x \notin \{-1, 3 \})?

    In other words, find a function \tilde{g}: \mathbb{R} \rightarrow \mathbb{R} such that \tilde{g} is continuous everywhere, and \tilde{g}(x) = g(x) for all x \notin \{-1, 3 \}.

    What you're dealing with is something called a "removeable discontinuity", for reasons you'll hopefully soon understand. For now, classify these problems under "So Simple They're Confusing".
    Last edited by johnsomeone; September 13th 2012 at 05:35 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2012
    From
    Maryland
    Posts
    45

    Re: How to make this piecewise continuous (multiple variables, lines)

    Quote Originally Posted by johnsomeone View Post
    f(x) = \frac{(x-3)(x-2)(x+1)}{(x+1)(x-3)}, x \notin \{-1, 3 \} already is peicewise continuous. I assume the problem is actually asking how to make it continuous.

    Here are some questions for you. I'm going to define a function on the same domain. Let g(x) = x-2, x \notin \{-1, 3 \}.

    First Question: What's the relationship, if any, between f and g?

    Second Question: Can you think of a continuous function defined on all of \mathbb{R} that equals g on g's domain of x \notin \{-1, 3 \})?

    In other words, find a function \tilde{g}: \mathbb{R} \rightarrow \mathbb{R} such that \tilde{g} is continuous everywhere, and \tilde{g}(x) = g(x) for all x \notin \{-1, 3 \}.

    What you're dealing with is something called a "removeable discontinuity", for reasons you'll hopefully soon understand. For now, classify these problems under "So Simple They're Confusing".
    I gotta be honest with you, I have no idea what you're talking about lol.

    It asks " Find the value of f k,m that will make f(x) continuous everywhere."

    I figure you'd have to set the functions equal to eachother and insert an x value to solve for p and then solve for m after setting the first and third functions equal to eachother.

    Am I wrong? How is this done. I have a test tommorow and I just found out there might be a question on this tommorow. (Although most will be straightfoward limits)
    Last edited by skinsdomination09; September 13th 2012 at 05:43 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    147

    Re: How to make this piecewise continuous (multiple variables, lines)

    OK, I thought you had 3 separate questions there. What you wrote didn't make much sense - I thought I'd deciphered it, but it seems I did so incorrectly.
    If you're going to get help, people will have to understand your problem. For instance, you said the problem was posed as "Find the value of f k,m that will make f(x) continuous everywhere." How can I help you find k when your post doesn't even have a k?
    Do you think you understand the problem you're asking about? - Not how to solve it, but what it even means? If you could clarify what the problem actually is, maybe we could try again.
    -----
    ?? Might the problem be asking this:

    f(x) = 4px - 2 when x < -1

    f(-1) = \ ?

    f(x) = \frac{(x-3)(x-2)(x+1)}{(x+1)(x-3)} when -1 < x < 3

    f(3) = \ ?

    f(x) = 5mx^2 - 2x when x > 3

    Find the values of m and p, and values of f(-1) and f(3), so that f is continuous. Could that be the problem?
    Last edited by johnsomeone; September 13th 2012 at 05:53 PM.
    Thanks from skinsdomination09
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 12th 2012, 03:38 PM
  2. Laplace Transform of a Continuous Piecewise Function
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 28th 2010, 04:27 PM
  3. Replies: 0
    Last Post: October 14th 2009, 11:16 AM
  4. Make Lines Parallel
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: August 20th 2009, 10:40 AM
  5. Piecewise continuous
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 30th 2008, 01:23 PM

Search Tags


/mathhelpforum @mathhelpforum