Point discontinuity problem

In summary, the conversation is about finding the value of p at which a discontinuity would occur in the function f(x) = x^2 - 6x + 9 / x - p. The person asking for help has been able to solve the problem for numerical values of p, but needs assistance with finding the value of p at which the discontinuity would occur. The conversation also includes a discussion about factorizing the function and the importance of using parentheses to avoid confusion. The person asking for help eventually solves the problem with the help of others.
  • #1
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Homework Statement



Find the value of p at which the discontinuity would occur.


Homework Equations



f(x) = x^2 - 6x + 9 / x - p

The Attempt at a Solution



Able to solve if p has an assigned numerical value, but help is needed for determining the value of p at which the discontinuity would occur. Any help is appreciated. Thank you.
 
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  • #2
Factorize [itex]x^2 - 6x + 9[/itex].
 
  • #3
Okay. Thanks; once I have done that, how would I solve for p?
 
  • #4
If you haven't yet found the answer to your other problem, I would suggest you do that and then come back to this problem, at which point the solution will hopefully be obvious.

In any event I would recommend re-reading the material on which these problems are based, since you don't seem to be fully comfortable with it.
 
  • #5
A discontinuity occurs when you cannot determine the function value at a certain argument(x) value. There's an operation only Chuck Norris can do..or so they say.

X-p , you know that there is one value that it can't have since it's in the denominator.
You also know that the function at 1st glance Could be 0 when X=?? according to the numerator.

What's the 1 value that cannot be P? Everything else can. Think of a hyperbole.
 
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  • #6
neuro.akn said:

Homework Statement



Find the value of p at which the discontinuity would occur.


Homework Equations



f(x) = x^2 - 6x + 9 / x - p

The Attempt at a Solution



Able to solve if p has an assigned numerical value, but help is needed for determining the value of p at which the discontinuity would occur. Any help is appreciated. Thank you.

As in your other posting: you need parentheses! If I read what you wrote using standard rules for mathematical expressions, I would see
[tex] f(x) = x^2 - 6x + \frac{9}{x} - p.[/tex]
 
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  • #7
Ray Vickson, (x^2 - 6x + 9) / (x - p)
Thank you all for your help.
 
  • #8
The thing is, we have not gone over this material at all.
 
  • #9
I have solved the problem. Thank you everyone.
 

What is a point discontinuity?

A point discontinuity is a type of discontinuity that occurs when a function has a break or gap at a single point, resulting in a jump or hole in the graph of the function.

What causes a point discontinuity?

A point discontinuity can be caused by various factors, such as a removable singularity, a jump or break in the function, or a vertical asymptote.

How is a point discontinuity different from other types of discontinuities?

A point discontinuity is different from other types of discontinuities, such as jump discontinuities or essential discontinuities, because it only occurs at a single point rather than a range of values.

Why is the point discontinuity problem important in mathematics?

The point discontinuity problem is important in mathematics because it can affect the behavior and accuracy of a function. It is crucial to identify and understand these discontinuities in order to properly analyze and interpret mathematical models and data.

How can we solve the point discontinuity problem?

The point discontinuity problem can be solved by using various techniques, such as finding the limit of the function, identifying and removing any removable singularities, or determining if there is a vertical asymptote present. It is also important to consider the context and domain of the function in order to fully understand and solve the problem.

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