## domain of the function f(x) = sqrt[5](7x^2 - 12x)

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mxmbulat
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### domain of the function f(x) = sqrt[5](7x^2 - 12x)

Please, help me with this equation f(x) = sqrt[5](7x^2 - 12x). I need to find the domain of this function and indicate it in interval notation.
While I know how to find domain of f(x) = sqrt(7x^2 - 12x) I am struggling with the first function.

stapel_eliz
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...f(x) = sqrt[5](7x^2 - 12x). I need to find the domain of this function and indicate it in interval notation.
While I know how to find domain of f(x) = sqrt(7x^2 - 12x) I am struggling with the first function.
By "sqrt[5]", do you mean "the fifth root of", or "5th-rt(7x^2 - 12x)"?

If so, think about odd-indexed roots. The restriction on square roots (and fourth roots and sixth roots and...) comes from the fact that you cannot have negatives inside those even-indexed roots. Is that the case for odd-indexed roots?

mxmbulat
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### Re: domain of the function f(x) = sqrt[5](7x^2 - 12x)

I mean this equation:

Yes, I know that one cannot have negatives in even-indexed roots, but I somehow found myself dumb at answering for the odd-indexed roots.

mxmbulat
Posts: 3
Joined: Sat Jan 21, 2012 11:21 pm
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### Re: domain of the function f(x) = sqrt[5](7x^2 - 12x)

Yes, I know that one cannot have negatives in even-indexed roots, but I somehow found myself dumb at answering for the odd-indexed roots.
Nevermind, following the logic that only even-indexed roots cannot have negatives, I assumed that in the case of the odd-indexed roots negatives can be inside the roots. Taking this into consideration, the domain of this function would be (-infinity, infinity).