Answer
The given relation does not define $y$ as a function of $x$.
domain: $[0, +\infty)$
range: $(-\infty, +\infty)$
Work Step by Step
For every positive value of $x$, the equation $x=y^4$ gives more than one value of $y$.
Example:
For $x=1$, the values of $y$ are $1$ and $-1$.
This means that for some values of $x$, $x$ is paired with two values of $y$.
Thus, the given relation does not define $y$ as a function of $x$.
The value of $x$ can be any non-negative real number so the domain is $[0, +\infty)$.
$y$ can be any real number.
Thus, the range is $(-\infty, +\infty)$ .
