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Suppose that A={0,1,2,3,4}, B={2,3,4,5}, f={(0,3),(1,3),(2,4),(3,2),(4,2)}

Find the domain and range of f. f(1)=? f(2)=?

My opinion is; f(1)=3 and f(2)=4

If I am right, what would be f(2) if there was also (2,3) in f? Edit: I read the definition of a function and I understand that (2,3) cannot be in f. Because, if it was, f would not be a function.

And my opinion is; the domain is {0,1,2,3,4} and the range is {2,3,4}

Finally, is codomain and range are the same thing?

Thank you :)

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You are right about what $ f (2) $ and $ f (1) $ equal. The range is $ {2,3,4} $. If there was a $(2,3) $ also, $ f $ wouldn't be a function. And yes codomain is the same as range.

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  • $\begingroup$ Thank you so much :) Finally, for f={(x,4x+5):x€Z}. Domain and Range is Z, and f(10) is 45, right? :) I just want to be sure.. $\endgroup$
    – AYARcom
    Aug 31 '14 at 20:42
  • $\begingroup$ @AYARcom It'a not a line no. And the way it is define above, $ f(10) $ doesn't exist because 10 is not apart of the domain you defined above, a.k.a $ A $. If you mean $\mathbb {Z} $, as in integers, the whole integers is not the domain and range. The function is not continuous it has a domain ${0,1,2,3,4 } $ and range ${2,3,4}$. The function is discrete. It only exists for what you defined above. $\endgroup$
    – dylan7
    Aug 31 '14 at 20:48
  • $\begingroup$ Oh, actually this was another question.. $\endgroup$
    – AYARcom
    Aug 31 '14 at 22:05
  • $\begingroup$ @AYARcom Oh, makes sense why I was confused. Yes $\mathbb {Z} $ is the domain and range of the function you just stated. $\endgroup$
    – dylan7
    Aug 31 '14 at 22:21

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