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Domain and Range using sets

  1. Sep 18, 2007 #1
    I was just wondering if you could write a functions domain and range with a set?

    Would it be something like

    D: {[tex]x \epsilon \mathbb{R}[/tex] | any condtitions}
    R: {[tex]f(x) \epsilon \mathbb{R}[/tex] | any condtitions}

    for any function f(x)?
  2. jcsd
  3. Sep 18, 2007 #2


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    Homework Helper

    What exactly is your question? Look at the definitions of "domain" and "range" (of a function). Of course they are sets. And of course that, in the definition of "range", some conditions must be satisfied, namely, R(f) = {f(x) : x is in the domain of f}.
  4. Sep 18, 2007 #3
    His question is simple, Can you write the domain and range of a function as sets. The answer is Yes, because they are sets.
  5. Sep 18, 2007 #4
    Thanks for the replies. I know that the domain and range are sets, I was more asking along the lines of is my set "notation" correct? Sorry, I should have asked that to begin with...
  6. Sep 19, 2007 #5


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    Science Advisor

    Should have asked what? If you know that "domain" and "range" of a function are sets, then of course they can be written in "set notation"!
  7. Sep 19, 2007 #6
    You don’t need to put “any condition” - the vertical bar should read “such that” so when you write a set ask yourself is what you wrote makes sense saying "such that" for |. Also you could just put R for your example of domain. If you gave the set you gave as range for an answer you should get 0 points. When a book ask you to find the range they are asking for the range specific to that function; yours just trys to restate the definition.

    Typically they will look something like

    R-{0} or something like {x | x >= 0 and x is an element of R}
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