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afievans Group Title

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

  • 8 months ago
  • 8 months ago

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  1. sleung Group Title
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    The domain is the set of all reals, since f(g(x))=x+1.

    • 8 months ago
  2. afievans Group Title
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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

    • 8 months ago
  3. sleung Group Title
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    You plug in the square root of x-1 for x.

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

    • 8 months ago
  5. afievans Group Title
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    oh great... this makes sense now. so what is the domain? hope I am asking the right question

    • 8 months ago
  6. sleung Group Title
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    x can be anything, so the domain is the set of all real numbers.

    • 8 months ago
  7. afievans Group Title
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    Thank you. you are a star!

    • 8 months ago
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