Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**princess snowwhite****Member**- Registered: 2012-11-06
- Posts: 29

f(x)= [x] + (x-[x])^2.

where [x] means largest integer not exceeding x.

then find set of all values taken by f

Offline

**princess snowwhite****Member**- Registered: 2012-11-06
- Posts: 29

I think the set will be infinite. does anyone has anything else in mind?

Offline

**zetafunc.****Guest**

Is [x] the floor function, then? (e.g. [6] = 6?)

**princess snowwhite****Member**- Registered: 2012-11-06
- Posts: 29

yes for n=2, [n]=2 but when n=1.6, [n]=1

Offline

**zetafunc.****Guest**

Then, I think f can take on any real value.

**princess snowwhite****Member**- Registered: 2012-11-06
- Posts: 29

so I . the set should be infininte

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,859

zetafunc. wrote:

Then, I think f can take on any real value.

That is true. You can even plot it to see that the range is R (ie. the reals).

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

Pages: **1**