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!

Conceptual question concerning functions

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data

    If I have a function that is not defined at a point in its domain is this the same as saying it is discontinuous?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 27, 2013 #2

    Mark44

    Staff: Mentor

    If it's not defined at some point, then that point is not in the domain of that function.

    If the function is not defined at some point, then it is discontinuous at that point.
     
  4. Feb 28, 2013 #3

    pasmith

    User Avatar
    Homework Helper

    No. If a function is not defined at a point, then that point is not in its domain. But a function can be continuous at each point of its domain notwithstanding that its domain consists of disjoint subsets of some larger set. For example, the following function is continuous everywhere in its domain:
    [tex]
    f : \mathbb{R} \setminus \{0\} \to \mathbb{R} : x \mapsto \left\{\begin{array}{r@{\qquad}l}
    0 & x < 0 \\
    1 & x > 0
    \end{array}\right.
    [/tex]
    On the other hand, there is no [itex]a \in \mathbb{R}[/itex] such that the following function is continuous at 0:
    [tex]
    g : \mathbb{R} \to \mathbb{R} : x \mapsto \left\{\begin{array}{r@{\qquad}l}
    f(x) & x \neq 0 \\
    a & x = 0
    \end{array}\right.
    [/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Conceptual question concerning functions
Loading...