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Fanduekisses

  • one year ago

*How to find the domain of a composite function?

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  1. Fanduekisses
    • one year ago
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    \[f(x)=\frac{ 1 }{ x^4-1 }\] \[g(x)=\sqrt[6]{x}\] \[g(f(x))=\sqrt[6]{\frac{ 1 }{ x^4-1 }}\]

  2. Fanduekisses
    • one year ago
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    Do I look at the radical or the denominator first?

  3. anonymous
    • one year ago
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    I don't think it matters, but I guess start with the inside function. I think either way you're looking for where \(x^4-1>0\)

  4. Fanduekisses
    • one year ago
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    It can't equal 0

  5. anonymous
    • one year ago
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    right it has to be greater than 0

  6. Fanduekisses
    • one year ago
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    because it's inside the radical or because it's in the denominator?

  7. Fanduekisses
    • one year ago
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    well, ok it doesn't matter lol

  8. anonymous
    • one year ago
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    both. It can't be equal to 0 because of the denominator. It can't be less than 0 because of the even radical

  9. Fanduekisses
    • one year ago
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    Ok so, first the f(x), its domain is x cannot equal -1 or 1 ?

  10. Fanduekisses
    • one year ago
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    Then how do I find the domain of g(f(x)) ?

  11. anonymous
    • one year ago
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    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|

  12. anonymous
    • one year ago
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    really you're just looking for the sign since the inequality is asking for positive values. Wherever it's positive will be the domain

  13. Fanduekisses
    • one year ago
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    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...

  14. Fanduekisses
    • one year ago
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    Can you please explain to me the rules of finding domain of a composition function?

  15. anonymous
    • one year ago
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    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|

  16. anonymous
    • one year ago
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    So since you're looking for the positive part, the domain is (-∞, -1) U (1, ∞)

  17. Fanduekisses
    • one year ago
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    So that is why you look at the domain of f(x) (inside) first? As like a guide?

  18. anonymous
    • one year ago
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    Yes

  19. Fanduekisses
    • one year ago
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    Ohhhhhhhhhh

  20. Fanduekisses
    • one year ago
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    It makes so much sense now, like the domain has to work for both functions and stuff.

  21. anonymous
    • one year ago
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    exactly

  22. Fanduekisses
    • one year ago
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    Thanks!

  23. anonymous
    • one year ago
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    you're welcome

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