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afievans

  • 2 years ago

Find the domain of the composite function f∘g. f(x)=x^2+2; g(x)=√x−1

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  1. sleung
    • 2 years ago
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    The domain is the set of all reals, since f(g(x))=x+1.

  2. afievans
    • 2 years ago
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    why is f(g(x)) = x+1 since the equation states f(g(x)) equals the square root of x-1

  3. sleung
    • 2 years ago
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    You plug in the square root of x-1 for x.

  4. sleung
    • 2 years ago
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    \[f(g(x))=(\sqrt{x-1})^{2}+2=(x-1)+2=x+1\]

  5. afievans
    • 2 years ago
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    oh great... this makes sense now. so what is the domain? hope I am asking the right question

  6. sleung
    • 2 years ago
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    x can be anything, so the domain is the set of all real numbers.

  7. afievans
    • 2 years ago
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    Thank you. you are a star!

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