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Thread: 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. :/

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

    Maximal Domain of $\displaystyle fog$ and $\displaystyle gof$


    ok so lets start with $\displaystyle fog$

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

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

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


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

    $\displaystyle gof$

    Domain of $\displaystyle f(x) = \Re$

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

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

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

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