Domain of x^2-6x+9 / x^2

  1. 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.
     
  2. jcsd
  3. Curious3141

    Curious3141 2,970
    Homework Helper

    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 ?
     
  4. HallsofIvy

    HallsofIvy 40,302
    Staff Emeritus
    Science Advisor

    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?"
     
  5. Undefined!
     
  6. HallsofIvy

    HallsofIvy 40,302
    Staff Emeritus
    Science Advisor

    And therefore, the domain of (x^2-6x+9 )/ x^2 is?
     
  7. Any value of x for which you can evaluate the term.
     
  8. Curious3141

    Curious3141 2,970
    Homework Helper

    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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