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HELP I do not understand!

  • Thread starter Math_Geek
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  • #1
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HELP!!! I do not understand!

1. Homework Statement
Define f(x)=2x, x is rational and x+3 when x is irrational. Find all points where g(x) is continuous and prove continuity at these points


2. Homework Equations
From analysis homework and using the real definition of continuity


3. The Attempt at a Solution

Graphing g(x) I can see that the only point that will be continuous will be at x=3, how would you show using the definition that this point is continuous. Also is this the only point. I have been struggling, please help a girl in distress. lol
 

Answers and Replies

  • #2
tiny-tim
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… 'tis I … tiny-tim! …

Graphing g(x) I can see that the only point that will be continuous will be at x=3, how would you show using the definition that this point is continuous. Also is this the only point. I have been struggling, please help a girl in distress. lol
:smile: … don't worry that pretty little head … :smile:

Just choose an epsilon, and find a delta such that f(3 + x) - 6 < epsilon, for all x < delta, and all your worries will go away! :smile:
 
  • #3
23
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so I just solve it like a limit problem? Thank you so much, I just knew someone would help a girl in distress lol.
 

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