Question

find the domain and range for |2x-1| / 2x-1

Answer 1

Well, there has to be something that is totally obvious to you concerning what x cannot equal

Answer 2

what do you mean?

Answer 3

What I mean is, you know that the denominator cannot equal a certain number or else the entire function would be undefined.

Answer 4

my intrnet connection is slow. sorry btw

Answer 5

so the domain is (-infinity, 1/2) u (1/2 , infinity)

Answer 6

i can find the domain but i have problem with the range

Answer 7

What problem is that?

Answer 8

the range of course

Answer 9

the range is all the possible y values. You know all the possible x values. You also know that you cannot have a range without knowing the domain. If the domain is the input into the function, and you have both the domain and function, and if every valid x in the domain corresponds to every valid y in the range, then you can figure out the range. You have already figured out what x cannot equal. You can find the range as simple as that without difficulty. You should not believe you cannot find the range if you already know the entire domain. It's like saying, you have the correct key to get in your home but you cannot get in.

Answer 10

so the answer should be all real number?

Answer 11

The answer cannot be all real numbers for the range because your domain is limited. You cannot have an unlimited range if your domain is limited.

Answer 12

If the x of a function is discontinuous along its domain, then the y of a function will also be discontinuous along its range.

Answer 13

Not written in a book anywhere but perfectly legitimate.

Answer 14

Bro, have you just given up?

Answer 15

not yet. i'm trying to searching for the answer and still i don't get it

Answer 16

You already know that the domain is only limited because x ≠ .5, otherwise the domain would be continuous. Now, using logic, you can reason that the same situation exists with the range. You can further reason that within the function there exists a point, (x,y) such that the function has a removable discontinuity. We already know the x value of this "discontinuous point" (.5,y). Find the y. If you're familiar with finding limits as x approach certain numbers, this should not be a difficult task.