What is the Domain of x^2-6x+9 / x^2?

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Homework Help Overview

The problem involves determining the domain of the function represented by the expression (x^2 - 6x + 9) / x^2. Participants are discussing the implications of the function's definition and the conditions under which it is valid.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question the necessity of defining the domain alongside the function. Others explore the implications of division by zero, particularly at x = 0, and discuss how this affects the validity of the function.

Discussion Status

The discussion is exploring various interpretations of the domain, with participants noting the importance of identifying values that make the function undefined. There is a focus on understanding the implications of the expression and how to represent the domain correctly.

Contextual Notes

Participants mention that the domain could vary depending on the context, such as whether the function is considered over the reals or other number systems. There is an emphasis on the need to exclude zero from the domain due to division by zero.

Rusho
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Here is the problem again
x^2-6x+9 / x^2

I think the answer is "all real numbers", but I don't know. I'm not used to seeing only x^2. Most of the ones I have done are x^2 - 4 or something like that.
 
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The question as it is written makes little sense. The domain has to be defined in the first place for a function to mean anything. So the domain can be a subset of the reals, or complex numbers, or even integers. Given a particular domain, it is a perfectly valid question to determine the range of the function.

But there is one real value for x where the function ceases to be well-defined, and I think the question is asking you to find this. What happens when x = 0 ?
 
As Curious3141 said, strictly speaking, the domain has to be "given" along with the formula describing a function. A lot of the time, however, it is understood that the domain is "all values of x for which the formula gives a valid result". One of the first things you should have learned about "domain" is "you can't divide by 0". Thus Curious3141's question "what happens when x= 0?"
 
Undefined!
 
And therefore, the domain of (x^2-6x+9 )/ x^2 is?
 
Any value of x for which you can evaluate the term.
 
A nice way of representing the domain is R\{0} which means all the reals except zero. Another way is to state the domain is [tex](-\infty,0) \cup (0,\infty)[/tex] because the open interval excludes the point at zero.

If you're working in a system other than the reals, amend accordingly.
 

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