# Question #f8d17

First of all, you have put this question in the wrong section. The answer for the domain is $x \in \mathbb{R}$ for $f \left(x\right) = {\left(x - 4\right)}^{\frac{1}{3}}$.
This is a different case than $f \left(x\right) = \sqrt{x - 4}$ because a real number times itself can never be negative, eg. $x \cdot x \ne - 2$. This is always the case with even roots.
However, it is not the case with odd roots. We can find an $x$ such that $x \cdot x \cdot x = - 8$, the answer is $x = - 2$. Therefore the domain is not restricted for odd roots.