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

[mxmbulat]

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]

...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]

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]

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).