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

In summary, the conversation discusses finding the points of discontinuity for a piece-wise function and determining whether it is left- or right-continuous at each point. The speaker is having trouble understanding the concept and has tried graphing it but still needs clarification. They are asked to show their work so far and consider the limits of the function.
  • #1
jennaskim
7
0
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?
 
Physics news on Phys.org
  • #2
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
 
  • #3
Well i tried graphing it...but I STILL DON'T UNDERSTAND
 
  • #4
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
 
  • #5
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
 
  • #6
You can start by considering these two limits :

[tex]lim_{x→1^-} f(x)[/tex]

and

[tex]lim_{x→1^+} f(x)[/tex]

What happens here?
 

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

What is a point of discontinuity?

A point of discontinuity is a point on a graph where the function is either undefined or has a jump in values. This means that the function is not continuous at that point.

How do you determine the points of discontinuity for a piecewise function?

To determine the points of discontinuity for a piecewise function, you need to check the values of the function at the boundary between the two pieces. In this case, we need to check the value of f(1) since the function changes at that point.

Is the function continuous at x = 1?

No, the function is not continuous at x = 1 since the function has a jump in values at that point.

What type of discontinuity does the function have at x = 1?

The function has a jump discontinuity at x = 1 since the value of the function changes abruptly from x + 1 to 1/x at that point.

Can a function have multiple points of discontinuity?

Yes, a function can have multiple points of discontinuity. In this case, the function has one point of discontinuity at x = 1, but it could have more depending on the function's behavior.

Similar threads

Is the given function continuous at x= 0? f(x) = {sin(1/x) if x≠0, 1
Replies
4
Views
3K
A few questions to make sure I understand Fourier series
Replies
3
Views
993
Find f s. t. ||f||=1 and f(x) < 1 with ||x||=1
Replies
19
Views
868
Discontinuous partial derivatives example
Replies
2
Views
322
Problem 1-23 and 1-24 from Spivak's Calculus on Manifolds
Replies
6
Views
1K
Prove that Lim x->c f(x)g(x)=0 if Lim x->c f(x)=0 and |g(x)|<K
Replies
2
Views
2K
f(x) = 2x+1, proving that it is continuous when p = 1 with 𝛿 and ε
Replies
7
Views
714
Proving piecewise function is k-differentiable
Replies
5
Views
953
Understanding the solution to a calculus problem (removable discontinuities)
Replies
2
Views
2K
Does each norm on vector space become discontinuous when restricted to S^1?
Replies
1
Views
910

Hot Threads

Recent Insights

Back
Top