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Math Help - Composite Functions

  1. #1
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    Composite Functions

    Hi,

    I am perfectly able to understand composite functions, given expressions for each function. Such as f(x) = x + 3, g(x) = 2x +1. Then f(g(x)) would be:
    (2x+3)+1 = 2x +4. Am I right?

    However, I don't know how to approach questions where only the elements in a function are stated. Like the following:

    Given A = {1, 2, 3, 4}, B = {a, b, c, d}:

    f(x) = {(1,b), (2,c), (3,d), (4,a)}
    g(x) = {(a,1), (b,2), (c,4), (d,4)}


    Find g(f(2)) and f(g(2)).

    Or rather, what does g(f(2)) and f(g(2)) mean?
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  2. #2
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    Re: Composite Functions

    Quote Originally Posted by aprilrocks92 View Post
    I don't know how to approach questions where only the elements in a function are stated. Like the following:
    Given A = {1, 2, 3, 4}, B = {a, b, c, d}:
    f(x) = {(1,b), (2,c), (3,d), (4,a)}
    g(x) = {(a,1), (b,2), (c,4), (d,4)}

    Find g(f(2)) and f(g(2)).
    Or rather, what does g(f(2)) and f(g(2)) mean?
    Look, at the definition (2,c)\in f or f(2)=c.

    Then g(f(2))=g(c) but (c,4)\in g so g(c)=4.

    Therefore g(f(2))=4

    Did you copy the problem correctly? Because f(g(2)) is not defined.

    It could be f(g(c))~?
    Last edited by Plato; October 3rd 2013 at 03:22 AM.
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