Thread: 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).

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 ?

If so, your friend is correct.

Just think about it in casses:

case 1:

case 2:

case 3:
.
.
.
Do this for every number in your interval.

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).

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).

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.

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