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**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

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

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

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**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

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**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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

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

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