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#1 2012-11-19 21:02:23

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

value of function

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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#2 2012-11-20 04:35:57

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

Re: value of function

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

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#3 2012-11-20 04:40:27

zetafunc.
Guest

Re: value of function

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

#4 2012-11-20 05:01:03

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

Re: value of function

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

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#5 2012-11-20 05:07:19

zetafunc.
Guest

Re: value of function

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

#6 2012-11-20 05:12:54

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

Re: value of function

so I smile. the set should be infininte

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#7 2012-11-20 06:21:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: value of function

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).


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