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

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SUMMARY

The discussion focuses on identifying points of discontinuity in the piecewise function f(x) = x + 1 for x < 1 and f(x) = 1/x for x ≥ 1. The primary point of discontinuity is at x = 1, where the left-hand limit (lim_{x→1^-} f(x) = 2) differs from the right-hand limit (lim_{x→1^+} f(x) = 1). Consequently, the function is neither left-continuous nor right-continuous at this point.

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  • Knowledge of limits in calculus
  • Familiarity with continuity concepts
  • Graphing techniques for functions
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  • Study the concept of limits in calculus, specifically one-sided limits
  • Learn about continuity and discontinuity in piecewise functions
  • Practice graphing piecewise functions to visualize discontinuities
  • Explore the implications of left-continuity and right-continuity in function analysis
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Students and educators in calculus, mathematicians analyzing piecewise functions, and anyone seeking to understand continuity and discontinuity in mathematical functions.

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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