Find the points of discontinuity: f(x) = x + 1 , for x < 1 and 1/x for x ≥ 1?

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Homework Help Overview

The problem involves identifying points of discontinuity in a piecewise function defined as f(x) = x + 1 for x < 1 and f(x) = 1/x for x ≥ 1. Participants are asked to determine the continuity of the function at the transition point.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express difficulty in understanding the function's behavior at the point of transition, with some attempting to graph the function. Questions arise regarding the limits from both sides of the transition point.

Discussion Status

The discussion is ongoing, with participants seeking clarification on their understanding of continuity and limits. Some have suggested examining the limits at the transition point, indicating a potential direction for further exploration.

Contextual Notes

Participants have been encouraged to show their work and describe their confusion, indicating a collaborative effort to clarify the problem without providing direct solutions.

jennaskim
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Find the points of discontinuity: f(x) = x + 1 , for x < 1 and 1/x for x ≥ 1?

^ supposed to be a piece-wise function.

State whether f is left- or right-continuous at each point of discontinuity.




I'm having difficulty figuring this out... please help?
 
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jennaskim said:
Find the points of discontinuity: f(x) = x + 1 , for x < 1 and 1/x for x ≥ 1?

^ supposed to be a piece-wise function.

State whether f is left- or right-continuous at each point of discontinuity.




I'm having difficulty figuring this out... please help?

Show you work so far.

RGV
 
Well i tried graphing it...but I STILL DON'T UNDERSTAND
 
jennaskim said:
Well i tried graphing it...but I STILL DON'T UNDERSTAND

Please explain exactly what you do not understand. We cannot guess about what is bothering you.

RGV
 
jennaskim said:
Well i tried graphing it...but I STILL DON'T UNDERSTAND

jennaskim, either draw your graph, or describe it

as Ray says, we need to see how far you've got, and what is confusing you
 
You can start by considering these two limits :

lim_{x→1^-} f(x)

and

lim_{x→1^+} f(x)

What happens here?
 

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