# Help with floor and ceiling functions

• Aug 1st 2009, 01:03 PM
kro
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).
• Aug 1st 2009, 02:06 PM
Danneedshelp
Quote:

Originally Posted by kro
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 $\displaystyle f(x)=2x-1$?

If so, your friend is correct.

Just think about it in casses:

case 1: $\displaystyle f(1)=[2(1)-1]=1$

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

case 3: $\displaystyle f(1.a)=[2(1.a)-1]=3$ $\displaystyle \Leftrightarrow$ $\displaystyle a>{5}$
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.
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Do this for every number in your interval.
• Aug 1st 2009, 02:50 PM
kro
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).
• Aug 1st 2009, 03:07 PM
Plato
Quote:

Originally Posted by kro
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).

$\displaystyle f(A)=\{1,2,3,4,5,6,7\}$
• Aug 1st 2009, 03:12 PM
Danneedshelp
Quote:

Originally Posted by kro
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.
• Aug 1st 2009, 03:35 PM
Plato
$\displaystyle \left\lceil {2x - 1} \right\rceil = \left\{ \begin{gathered} 1,\;x = 1 \hfill \\ 2,\;1 < x \leqslant 1.5 \hfill \\ 3,\;1.5 < x \leqslant 2 \hfill \\ \vdots \hfill \\ 7,\;6.5 < x \leqslant 4 \hfill \\ \end{gathered} \right.$
• Aug 9th 2009, 10:30 PM
pretygirl
I was registered at your forum. I have printed the test message. Do not delete, please.

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