Proving Continuity of g(x) at x=3: Using Real Definition and Limit Method

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In summary, the conversation is about finding points where g(x) is continuous and proving continuity at those points. The speaker is struggling to show that x=3 is the only point of continuity and asks for help. Another person offers a solution involving choosing an epsilon and finding a delta to solve the problem. The speaker expresses gratitude for the help.
  • #1
Math_Geek
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HELP! I do not understand!

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


Homework Equations


From analysis homework and using the real definition of continuity


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
 
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  • #2
… 'tis I … tiny-tim! …

Math_Geek said:
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
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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