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Math Help - compositions with sq roots

  1. #1
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    compositions with sq roots

    trying to insert f(x)=sq root x-3 into g(x)=sq root x^2+ 3 (GoF and FoG) but not sure how to get rid of the square roots
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  2. #2
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    Hello, vinson24!

    Given: . \begin{array}{ccc}f(x)&=& \sqrt{x-3} \\g(x) &=& \sqrt{x^2+ 3} \end{array}

    Find: . f\circ g\:\text{ and }\:g\circ f

    f\circ g \;\;=\;\;f(g(x)) \;\;=\;\;f(\sqrt{x^2+3}) \;\;=\;\;\sqrt{\sqrt{x^2+3}-3}

    g\circ f \;\;=\;\;g(f(x)) \;\;=\;\;g(\sqrt{x-3}) \;\;=\;\;\sqrt{(\sqrt{x-3})^2 + 3} \;\;=\;\;\sqrt{(x - 3) + 3} \;\;=\;\;\sqrt{x}



    Edit: misread the problem . . . corrected now (I hope).
    .
    Last edited by Soroban; September 2nd 2008 at 07:24 PM.
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  3. #3
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    the x^2 + 3 is in a sq root too or does it not matter
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  4. #4
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    thanks so much, i didnt think that first one simplified but wasnt quite sure
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