Fanduekisses
  • Fanduekisses
*How to find the domain of a composite function?
Mathematics
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Fanduekisses
  • Fanduekisses
*How to find the domain of a composite function?
Mathematics
jamiebookeater
  • jamiebookeater
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Fanduekisses
  • Fanduekisses
\[f(x)=\frac{ 1 }{ x^4-1 }\] \[g(x)=\sqrt[6]{x}\] \[g(f(x))=\sqrt[6]{\frac{ 1 }{ x^4-1 }}\]
Fanduekisses
  • Fanduekisses
Do I look at the radical or the denominator first?
anonymous
  • anonymous
I don't think it matters, but I guess start with the inside function. I think either way you're looking for where \(x^4-1>0\)

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Fanduekisses
  • Fanduekisses
It can't equal 0
anonymous
  • anonymous
right it has to be greater than 0
Fanduekisses
  • Fanduekisses
because it's inside the radical or because it's in the denominator?
Fanduekisses
  • Fanduekisses
well, ok it doesn't matter lol
anonymous
  • anonymous
both. It can't be equal to 0 because of the denominator. It can't be less than 0 because of the even radical
Fanduekisses
  • Fanduekisses
Ok so, first the f(x), its domain is x cannot equal -1 or 1 ?
Fanduekisses
  • Fanduekisses
Then how do I find the domain of g(f(x)) ?
anonymous
  • anonymous
You put the 1 and -1 on a number line. Put numbers on either side of them into the function to see where its positive. So find g(f(-2)), g(f(0)), and g(f(2)).|dw:1443058002457:dw|
anonymous
  • anonymous
really you're just looking for the sign since the inequality is asking for positive values. Wherever it's positive will be the domain
Fanduekisses
  • Fanduekisses
erhh I'm confused. :( or I'm exhausted, Idk why I'm finding this so confusing and it's probably not that hard to understand...
Fanduekisses
  • Fanduekisses
Can you please explain to me the rules of finding domain of a composition function?
anonymous
  • anonymous
There aren't any specific rules for composite functions. You have to look at the function once it's composed and try to figure out values excluded from the domain. For this function there's both a radical and rational parts. So it turns out that you'll have to solve a polynomial inequality to get the values. Plugging in -2, 0, and 2 into \(x^4-1\). \((-2)^4-1=15\) \(0^4-1=-1\) \(2^4-1=15\) Put the sign on the number line|dw:1443058814223:dw|
anonymous
  • anonymous
So since you're looking for the positive part, the domain is (-∞, -1) U (1, ∞)
Fanduekisses
  • Fanduekisses
So that is why you look at the domain of f(x) (inside) first? As like a guide?
anonymous
  • anonymous
Yes
Fanduekisses
  • Fanduekisses
Ohhhhhhhhhh
Fanduekisses
  • Fanduekisses
It makes so much sense now, like the domain has to work for both functions and stuff.
anonymous
  • anonymous
exactly
Fanduekisses
  • Fanduekisses
Thanks!
anonymous
  • anonymous
you're welcome

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