Calculus
posted by Anonymous on .
I'm doing graphs/domain/range of basic functions. I have three questions:
How do I find the domain and range of a function? (more preferably range...I'm okay but shaky on domain)
Ex: f(x)=1/(x^2)
Also, how do you write the domain and range with notation? Like when you use symbols like
(infinity, 0) U (0, infinity)
Specifically, how do I write "All real #'s where x cannot equal..."?
One more thing: what does [[x]] mean? The symbol looks like two brackets very close together or something.
Thank you very much!

Domain is the set of valid values as input to the function. In the particular example,
f(x)=1/(x^2)
x can take on all values except ±∞ and 0.
So the domain is (∞,0)∪(0,+&infin)
which means that the domain can take on all values from (but excluding) ∞ to (but excluding) zero, and from (but excluding) zero to (but excluding +∞.
The range is the interval of possible values when the function is evaluated. In the particular example, the range is (0,+∞). The evaluated function cannot take on negative values as x is squared.
Numerous articles are available for the description of interval notation. Basically, an interval is described by the lower and upper limits, separated by a comma. If the lower limit is included in the interval, a square left bracket is used. If it is to be excluded, a praenthesis (round bracket) is used. The same goes for the upper bound (right bracket.) For example,
[5,+∞) ranges from and including 5 to but excluding infinity.
For more detailed descriptions, see:
http://en.wikipedia.org/wiki/Interval_(mathematics)
http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html
http://en.wikipedia.org/wiki/Domain_of_a_function
I have not come across the [[x]] notation. Please give more information or context of its use. 
Thanks for the domain and range info!
Regarding the [[x]] symbol, the function is simply y = [[x]]. There isn't a symbol like that on my calculator (TI89).
I want to say that this may be the same as brackets, which I believe means absolute value. But what would be the difference between y = lxl and y = [x]?
I'm honestly not sure either... 
Sorry, I still don't have more information on [[x]]. If you have the answer or someone else has, please post and share the information.