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Math Help - Natural domain question

  1. #1
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    Natural domain question

    What is the natural domain of f(x) = x^2-4x+5?

    I tried using the quadratic formula, but there is a negative under the square root, so what is the domain?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by brumby_3 View Post
    What is the natural domain of f(x) = x^2-4x+5?

    I tried using the quadratic formula, but there is a negative under the square root, so what is the domain?

    What exactly do you ask for?. Perhaps: f(x)=(x-2)^2+1 so, if x\in\mathbb{Z} then, f(x)\in\mathbb{N} .
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  3. #3
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    You can square any number, you can add and subtract any numbers. The "natural domain" of any quadratic function (or, for that matter, of any polynomial function) is "all numbers". You talk about using the quadratic formula and a negative under the square root which is going the wrong way- you might use that to find the range. But it would be simpler to complete the square and find the vertex of the graph to do that.
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