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Math Help - functions.

  1. #1
    Newbie pedroiscool7's Avatar
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    functions.

    what are functions?
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  2. #2
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    Functions are one-to-one and onto mappings from a set A to a set B.

    \displaystyle f:A\rightarrow B

    Functions also have an inverse.

    Example \displaystyle e^x is the inverse to \displaystyle ln(x)
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  3. #3
    Member rtblue's Avatar
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    Here is a beginner's guide to functions:

    Functions versus Relations
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  4. #4
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    Quote Originally Posted by dwsmith View Post
    Functions are one-to-one and onto mappings from a set A to a set B.

    \displaystyle f:A\rightarrow B

    Functions also have an inverse.

    Example \displaystyle e^x is the inverse to \displaystyle ln(x)
    This is not true. The standard definition of function does NOT require "one to one" nor "onto". A function, from set A to set B, is a set of ordered pairs, (x, y), with x from A, y from B, such that we do not have two distinct ordered pairs with the same first element- that is, we cannot have (x, y1), (x, y2) with the same x but different y1 and y2. In more common terms that means that a function assigns a value of y, from set B, to every x in set A such that we do NOT assign different values of y to the same x.

    Here's what Wikipedia says: http://en.wikipedia.org/wiki/Function_(mathematics)
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  5. #5
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    Strictly speaking, a "well-defined" function associates one, and only one, output to any particular input.

    If not, then it is a multivalued-function. Multivalued function - Wikipedia, the free encyclopedia

    My definition corresponds to, as wikipedia calls it, a well-defined function then.
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  6. #6
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    Sorry, but, no, it doesn't. Yours corresponds to "invertible function". The function, for example, f(x)= x^2, is a "well defined function", with one and only one output to a particular input but is NOT "one to one and onto" because it does not asociate one and only one input with a particular output.
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