anonymous
  • anonymous
FIND f(g(x)) and g(f(x)) and each of the domains? f(x)=sqrt(x+4) , g(x)=x^2 -4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Luigi0210
  • Luigi0210
Do you know how to start?
anonymous
  • anonymous
I know how to solve them, but I mostly need help with finding the domains. Would you substitute g(x) for x in f(x) and vice versa? Both times getting x after simplifying?
anonymous
  • anonymous
\[f(x)=\sqrt{x+4}~~~~~~~~~g(x)=x^2-4\] So \[f(g(x))=\sqrt{(x^2-4)+4}=\sqrt{x^2}=|x|,~~\text{not }x\] and \[g(f(x))=\left(\sqrt{x+4}\right)^2-4=x+4-4=x\]

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anonymous
  • anonymous
Right, and the x in f(g(x)) would be in between the absolute values, because it was in a square root?
anonymous
  • anonymous
Yeah. It has to do with the sign on the inside of the square root. Can't have \(x^2<0\). But the domains of the composite functions don't depend on \(x\) or \(|x|\), but the domains of the component functions.

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