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onegirl

  • 3 years ago

Find all discontinuities of f(x). For each discontinuity that is removable, define a new function that removes the discontinuity. f(x) = x - 1/x^2 - 1

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  1. tkhunny
    • 3 years ago
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    First, please remember your Order of Operations. You have NOT written \(\dfrac{x-1}{x^{2}-1}\). Give it another go and use more parentheses. Denominator = 0 -- Discontinuity. Is it an Asymptote or NonRemovable Discoutinuity? Numerator = 0 AT THE SAME PLACE, this it's Removable and NOT an Asymptote.

  2. onegirl
    • 3 years ago
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    non removable

  3. tkhunny
    • 3 years ago
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    ?? There are two. 1) Which one are you talking about. 2) What's the other one?

  4. onegirl
    • 3 years ago
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    removable discontinuity or infinite

  5. onegirl
    • 3 years ago
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    so it will be replacing 0 will give you discontity right? and not any other number?

  6. tkhunny
    • 3 years ago
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    Please make a better effort to use complete sentences and to be substantially more clear. I'll do a quick example. Sentences, paragraphs, examples, order. Working with the Denominator: \(x^{2} - 1 = (x+1)(x-1)\) This denominator takes on the value zero at x = 1 and x = -1. These values are NOT in the Domain and are discontinuities. We do not yet know what kind of discontinuity. Working with the Numerator x - 1 = 0 when x = 1 This is enough information. x = 1 makes both Numerator and Denominator zero. This is, therefore, a removable discontinuity. Our original expression is equivalent to 1/(x+1) everywhere EXCEPT x = 1. x = -1 makes only the denominator zero. This is, therefore, an asymptote or infinite discontinuity. Now, we are done.

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