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Math Help - Help with floor and ceiling functions

  1. #1
    kro
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    Question Help with floor and ceiling functions

    Need help with the questions below:

    Suppose f : R Z where f(x) = the ceiling of 2x − 1.
    (a) If A = {x | 1 ≤ x ≤ 4}, find f(A).
    For this one I got {1,3,5,7} but one of my friends got {1,2,3,4,5,6,7}. Which one is right?
    (c) If C = {−9,−8}, find f−1(C).
    For this one I got -2 for both but somebody else got (-9/2, -7/2]. Which one is right?
    (d) If D = {0.4,0.5,0.6}, find f−1(D).
    For this one I got {4,3} but somebody else got the empty set/nullset. Which one is right?


    Suppose f : R R where f(x) = floor of x/2.
    (b) If T = {3,4,5}, find f−1(T).
    For this one I got zero for all three and somebody else got [6,12).
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  2. #2
    Senior Member Danneedshelp's Avatar
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    Quote Originally Posted by kro View Post
    Need help with the questions below:

    Suppose f : R Z where f(x) = the ceiling of 2x − 1.
    (a) If A = {x | 1 ≤ x ≤ 4}, find f(A).
    For this one I got {1,3,5,7} but one of my friends got {1,2,3,4,5,6,7}. Which one is right?
    a)

    I assume you mean f(x)=2x-1?

    If so, your friend is correct.

    Just think about it in casses:

    case 1: f(1)=[2(1)-1]=1

    case 2: f(1.a)=[2(1.a)-1]=2 \Leftrightarrow a\leq{5}

    case 3: f(1.a)=[2(1.a)-1]=3 \Leftrightarrow a>{5}
    .
    .
    .
    Do this for every number in your interval.
    Last edited by Danneedshelp; August 1st 2009 at 10:34 PM.
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  3. #3
    kro
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    The ceiling

    For the question below, it's the CEILING of 2x - 1.

    Suppose f : R Z where f(x) = the ceiling of 2x − 1.
    (a) If A = {x | 1 ≤ x ≤ 4}, find f(A).
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  4. #4
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    Quote Originally Posted by kro View Post
    For the question below, it's the CEILING of 2x - 1.

    Suppose f : R Z where f(x) = the ceiling of 2x − 1.
    (a) If A = {x | 1 ≤ x ≤ 4}, find f(A).
    f(A)=\{1,2,3,4,5,6,7\}
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  5. #5
    Senior Member Danneedshelp's Avatar
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    Quote Originally Posted by kro View Post
    For the question below, it's the CEILING of 2x - 1.

    Suppose f : R Z where f(x) = the ceiling of 2x − 1.
    (a) If A = {x | 1 ≤ x ≤ 4}, find f(A).
    Try following what I posted, you will get the same result as Plato and your friend. Just start at 1 and look at every case till you get to 4.
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  6. #6
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    <br />
\left\lceil {2x - 1} \right\rceil  = \left\{ \begin{gathered}<br />
  1,\;x = 1 \hfill \\<br />
  2,\;1 < x \leqslant 1.5 \hfill \\<br />
  3,\;1.5 < x \leqslant 2 \hfill \\<br />
   \vdots  \hfill \\<br />
  7,\;6.5 < x \leqslant 4 \hfill \\ <br />
\end{gathered}  \right.
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  7. #7
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    I was registered at your forum. I have printed the test message. Do not delete, please.

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