Because it is a cubic root, the argument can be positive and negative, so the domain is the set of all real numbers.
Here we have the function:
[tex]f(x) = \sqrt[3]{\frac{1}{2}*x - 10}[/tex]
Now, if this is a cubic root (as I understand what you wrote) then we can use any value of x inside of that function, because the degree is odd.
Is not the case of the square root, where the argument must only be positive.
With that in mind, we conclude that the domain is the set of all real numbers.
If you want to learn more about domains:
https://brainly.com/question/1770447
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