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Fanduekisses
 one year ago
*How to find the domain of a composite function?
Fanduekisses
 one year ago
*How to find the domain of a composite function?

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Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x)=\frac{ 1 }{ x^41 }\] \[g(x)=\sqrt[6]{x}\] \[g(f(x))=\sqrt[6]{\frac{ 1 }{ x^41 }}\]

Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0Do I look at the radical or the denominator first?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't think it matters, but I guess start with the inside function. I think either way you're looking for where \(x^41>0\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right it has to be greater than 0

Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0because it's inside the radical or because it's in the denominator?

Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0well, ok it doesn't matter lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0both. It can't be equal to 0 because of the denominator. It can't be less than 0 because of the even radical

Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0Ok so, first the f(x), its domain is x cannot equal 1 or 1 ?

Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0Then how do I find the domain of g(f(x)) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You 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
 one year ago
Best ResponseYou've already chosen the best response.0really you're just looking for the sign since the inequality is asking for positive values. Wherever it's positive will be the domain

Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0erhh 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
 one year ago
Best ResponseYou've already chosen the best response.0Can you please explain to me the rules of finding domain of a composition function?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0There 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 \(x^41\). \((2)^41=15\) \(0^41=1\) \(2^41=15\) Put the sign on the number linedw:1443058814223:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So since you're looking for the positive part, the domain is (∞, 1) U (1, ∞)

Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0So that is why you look at the domain of f(x) (inside) first? As like a guide?

Fanduekisses
 one year ago
Best ResponseYou've already chosen the best response.0It makes so much sense now, like the domain has to work for both functions and stuff.
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