Question

How do you write the range and domain of this f(x)=2[[x+1]]-1? it is a greatest integer function

Answer 1

the domain is the set of all workable inputs ....

the range, well, its all the outputs that are possible from the domain set

Answer 2

how would you write it in interval form?

Answer 3

well, to start with ... what do you determine the domain and range to be?

Answer 4

the domain would be all real numbers and the range would be all even numbers... but I don't know how to put it in interval form

Answer 5

range is all odd numbers, and yeah, putting that in interval notation seems a bit, well, odd

Answer 6

2n is an even number

2n-1 is an odd number

Answer 7

how would you put it in like the thing with the brace? R={y/y=all even numbers} something like this

Answer 8

a union of odds

... U [-3] U [-1] U [1] U [3] U ...

hmm

Answer 9

set notation, you just define the set

R = {y:y is an odd number}

Answer 10

or R={y : y=2n-1, for n in Z}

Answer 11

ohhh that's the thing i remember thanks; last one to be sure haha; y=4[[-3x+1]]+1 how about the range of this?

Answer 12

ideally its just 4n + 1, for an integer n

Answer 13

why is it 4?

Answer 14

because 4, times something, plus 1 is well .... defined for you already

Answer 15

-3x + 1 is just going to give us 'some integer'

Answer 16

ahh so you would just disregard the numbers inside the brackets?

Answer 17

well, disregard is a bad term to apply to it.

the brackets simply give us 'some integer' value to work with

Answer 18

oh oh oh how about this then? [[x]]+x

Answer 19

4n+1 is another way to say that y is eqaul to, 1 mod 4

Answer 20

what are your thoughts about the last one you posted?

Answer 21

i think it's right, thanks for your replies btw.

Answer 22

youre welcome

y = [[x]]+x

what does an integer, plus some real number, return to us?

Answer 23

even numbers?

Answer 24

or i don't know

Answer 25

(2.39384) + 2.39384

3 + 2.39384

you can output any real number since you are adding any real number to some integer

Answer 26

http://www.wolframalpha.com/input/?i=y+%3D+ceil%28x%29%2Bx

my initial thought is it is in error. there are gaps in the range

Answer 27

but the graph behaves like this

Answer 28

im not sure how we could define the range for it.