Suppose $f : \Bbb R →\Bbb R$ where $f(x) = \lfloor x/2 \rfloor$

Question

could someone please explain me how they got this answer ? im trying to figure out enter image description here

Do you know that $\lfloor \ \cdot \ \rfloor$ means? – Git Gud Mar 11 '13 at 22:11 — Git Gud, Mar 11 '13 at 22:11
I do...just no sure how did they get 6 and 12 in part b ? – Agape Twentyone Mar 11 '13 at 22:35 — Agape Twentyone, Mar 11 '13 at 22:35

score 3 · Accepted Answer · answered Mar 11 '13 at 22:18

3

The function $G(x)=\lfloor x\rfloor$ means that given $x$, $G(x)$ is the largest integer $k\in\Bbb Z$ such that $k\leq x$. For example, $\lfloor 1.5\rfloor=1$ and $\lfloor\pi\rfloor=3$.

In your question you need to calculate what is $\{\lfloor x/2\rfloor\mid 1\leq x\leq 6\}$, and what is the set $\{x\in\Bbb R\mid \lfloor x/2\rfloor=3\text{ or } 4\text{ or } 5\}$.

Let me give you some example, the set $\{x\in\Bbb R\mid \lfloor x/2\rfloor=0\}$ is the set of those real numbers $r$ that $0\leq r/2<1$, which in turn is exactly to say $0\leq r<2$.

I hope that this helps you understand what you are supposed to be doing, and how to do that.

answered Mar 11 '13 at 22:18

Asaf Karagila

393,674

thanks...i understood the a part....no sure about part b ...how did they get 6 and 12 in part b ? thanks – Agape Twentyone Mar 11 '13 at 22:32
1

Well, you really just have to sort of "stick the parts together". Try to see which number are sent to $3$ and which numbers are sent to $4$, and which numbers are sent to $5$. Then take the union of those three sets. – Asaf Karagila Mar 11 '13 at 22:36

Suppose $f : \Bbb R →\Bbb R$ where $f(x) = \lfloor x/2 \rfloor$

1 Answers1