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Are (x^2)/x and x the same?

  1. Sep 17, 2012 #1
    Suppose I have a function f defined on x, f(x) = (x^2)/x and another function g defined on x, g(x) = x. Are both these functions the same?

    I mean, when you try to determine the Domain of a function, do you simplify it as much as possible, and then find the Domain? Or find the Domain on the face of the function?

    In this case, what I think is that f has Domain-->ℝ-{0}, while g has Domain--> ℝ. Is this correct?
  2. jcsd
  3. Sep 17, 2012 #2
    No, they are not the same. Indeed, f is not defined in 0, while g is.

    However, f(x) and g(x) are the same for all nonzero x.
  4. Sep 17, 2012 #3


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    But of course, you can simplify without altering domains.

    [tex] f(x) = g(x), ~ \forall x, ~ \mbox{if} ~ f(x)=1 ~ \mbox{and} ~ g(x) = \frac{x^2 +1}{x^2 +1} [/tex]

    Bottom line, find the domain and see if it changes by any possible factoring/simplification.
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