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Math Help - Domain

  1. #1
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    Domain

    Find the natural domain of the function gf.

    f(x)= √x g(x)= x-5

    Thanks.
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  2. #2
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    Quote Originally Posted by Oasis1993 View Post
    Find the natural domain of the function gf.

    f(x)= √x g(x)= x-5

    Thanks.
    g(f(x)) = f(x) - 5 = \sqrt{x} - 5.

    The implied domain is clearly x \geq 0.
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  3. #3
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    But I would have interpreted "gf" as the product, (x- 5)\sqrt{x} which also has natural domain x\ge 0. The composition the other way, f\circ g(x)= \sqrt{x- 5}, on the other hand, has natural domain x\ge 5.
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