# Thread: Help with floor and ceiling functions

1. ## 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).

2. 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 $f(x)=2x-1$?

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.

3. ## 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).

4. 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).
$f(A)=\{1,2,3,4,5,6,7\}$

5. 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.

6. $
\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.$

7. I was registered at your forum. I have printed the test message. Do not delete, please.

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