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Math Help - Composite functions.

  1. #1
    Junior Member
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    Composite functions.

    Hi people, as you can see i am new in forum.

    I just learn today how to solve the domain of composite functions in internet.

    I tried to resolve one exercise, and i want to know if i solved it correctly. :/

    f(x) = x^2-3x
    g(x) =  \surd(x+2)

    Maximal Domain of fog and gof


    ok so lets start with fog

    domain of g(x) is x\geq-2

    f(g(x)) = x+2 - 3\surd(x+2)

    there are no restrictions so the composite domain is x\geq-2


    ----------------------------------------------------------------------------------------------

    gof

    Domain of f(x) = \Re

    g(f(x)) =   \surd(x^2-3x+2)
    the function creates new restrictions so domain is x\leq1 \cap x\geq2

    ------------------------------------------------------------------------------------------------

    These domain solutions are correct ?
    Sorry my english btw.
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  2. #2
    MHF Contributor
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    Re: Composite functions.

    Welcome.

    These domain solutions are correct ?
    Yes, except that \cap denotes an intersection of sets, while here we need a union. The answer to the second problem is \{x\in\mathbb{R}\mid x\le1\}\cup\{x\in\mathbb{R}\mid x\ge2\} or something like (-\infty,1]\cup[2,\infty).
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  3. #3
    Junior Member
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    Re: Composite functions.

    Quote Originally Posted by emakarov View Post
    Welcome.


    Yes, except that \cap denotes an intersection of sets, while here we need a union. The answer to the second problem is \{x\in\mathbb{R}\mid x\le1\}\cup\{x\in\mathbb{R}\mid x\ge2\} or something like (-\infty,1]\cup[2,\infty).

    Ok thanks for the help
    Thanks for showing me the error.
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