Range of a f(x) involving floor

[SneakyArab]

Homework Statement

I have to find the range of f(x) where:
f(x)=7*floor(x) - floor(7*x)
x is a real number.

Then I have to prove that this set of numbers is correct.

The Attempt at a Solution

I am still on the range part, and thus am only asking about that part at the moment. It seems to me that the range of f(x) would be (-infinity,+infinity). Is there a reason that it wouldn't be?

 

[slider142]

Sketch the graphs of g(x) = 7*floor(x) and h(x) = floor(7x) on the same paper.

 

[SneakyArab]

Ah yes, back to basics for me.

Ok so it seems that all possible values of f(x) are:
-6,-5,-4,-3,-2,-1,0;

thus range of f(x) = (-6,0).

Correct?

 

[discrete]

what does that round thing at the end of question #4 a and #4 b mean sneakyArab

 

[SneakyArab]

what does that round thing at the end of question #4 a and #4 b mean sneakyArab

seems I've found a classmate.

I'm not sure if you mean the last symbol or next to last, so after the equation it reads:

"is not rational"


so its not a rational number.

 

[SneakyArab]

I think I have a working proof on this one now. Thanks for getting me started Slider!

 

[discrete]

thanks man it looks all crazy i couldn't figure it out
good luck and thanks again