1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Functions - Range vs Codomain

  1. Feb 9, 2007 #1


    User Avatar
    Gold Member

    Hi. This isnt directly a homework question, but it will help in general.

    Im having a little trouble understanding what the difference between a range and codomain is. For example, for the function [tex]f(x) = \frac{3}{{2x - 2}}[/tex], i understand that the domain is [tex]\{ x \in R:x \ne 1\}[/tex]. Now, i also believe that the possible values that can be outputted by the function is given by
    \{ f(x) \in R:f(x) \ne 0\}
    [/tex]. Is this the codomain or range?

    Thanks in advance,
  2. jcsd
  3. Feb 9, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    The range/codomain is the image of the domain through the function

    [tex] \mbox{Ran}(f(x)):=\left\{ f(x)\left|\right x\in D(f(x)) \right\} [/tex]

    In your case, first make a plot of the function first.
  4. Feb 9, 2007 #3
    that is the range of the function. codomain is usually a superset (sometimes equal as well) of the range. its generally defined in the question itself, like f:R-->R (here both domain and codomain are the set of real nos.),but range will be a subset(or an equal set) of R depending upon the function definition.
  5. Feb 9, 2007 #4


    User Avatar
    Science Advisor

    According to Wikipedia, the "codomain" of a function f:X-> Y is the set Y. The "range" is the subset of Y that f actually maps something onto.

    For example, if f:R->R is defined by f(x)= ex, then the "codomain" is R but the "range" is the set, R+, of all positive real numbers.

    Notice that you cannot tell the "codomain" of a function just from its "formula". I could just as easily define f:R->R+, with f(x)= ex. Now the codomain and domain would be the same.
  6. Feb 21, 2011 #5
    I have a doubt, I think we also cannot tell what the "domain" is just from the "formula" . We can say what it "is not" but we cant say what it "is".

    for instance we can define a function as f:[1,2]->R , with f(x) = ex . here "domain" is what we define(i.e [1,2]) ,"co-domain" is what we define(i.e R) , but "range" is obtained from the formula, which in this case would be [e,e^2]

    but the formula definitely can tell us what domain is not.
    ex :- f(x) = [tex]\sqrt{x}[/tex] we can't say domain is R. we have to define domain as R[tex]^{+}[/tex] or it's subsets.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook