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Thread: Domain of Functions

  1. #1
    Senior Member harpazo's Avatar
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    Domain of Functions

    Find the domain of f(x) = -3x^2 + 5x.

    How is this done algebraically?
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    MHF Contributor MarkFL's Avatar
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    Re: Domain of Functions

    The given function has no even radicals or potential for division by zero, or anything else which would cause output to be undefined, so its domain is all reals.
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    Re: Domain of Functions

    Quote Originally Posted by harpazo View Post
    Find the domain of f(x) = -3x^2 + 5x.
    How is this done algebraically?
    It cannot done algebraically whatever that is.
    One must understand the concepts involved.
    But again you seem very reluctant to try that approach.
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    Senior Member harpazo's Avatar
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    Re: Domain of Functions

    Quote Originally Posted by MarkFL View Post
    The given function has no even radicals or potential for division by zero, or anything else which would cause output to be undefined, so its domain is all reals.
    Is there a difference between an even and odd radical?
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    MHF Contributor MarkFL's Avatar
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    Re: Domain of Functions

    Quote Originally Posted by harpazo View Post
    Is there a difference between an even and odd radical?
    Yes, an odd radical, such as a cube or fifth root, can have a negative radicand, where as an even radical like a square or fourth root cannot, when we are talking about real number function values.
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    Senior Member harpazo's Avatar
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    Re: Domain of Functions

    Quote Originally Posted by MarkFL View Post
    Yes, an odd radical, such as a cube or fifth root, can have a negative radicand, where as an even radical like a square or fourth root cannot, when we are talking about real number function values.
    Good. What about if we are talking about complex number function values? Am I stepping into an area considered advanced algebra?
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    Re: Domain of Functions

    Quote Originally Posted by harpazo View Post
    Good. What about if we are talking about complex number function values? Am I stepping into an area considered advanced algebra?
    The real number field is ordered. In it we can have upper & lower bounds.
    The complex number field is not ordered (cannot be ordered in the same sense).
    In the complex number field functions still have domains. However the word "range" suggest order, therefore we tend to use image instead.
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    Senior Member harpazo's Avatar
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    Re: Domain of Functions

    Good notes.
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