#### Answer

$y \text{ is NOT a function of }x
\\\text{Domain: }
[0,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To determine if the given equation, $
x=y^6
,$ is a function, solve first for $y$ in terms of $x.$ Then check if $x$ is unique for every value of $y.$
To find the domain, find the set of all possible values of $x.$
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
x=y^6
\\\\
y^6=x
\\\\
y=\pm\sqrt[6]{x}
.\end{array}
If $x=64,$ then $y=2$ or $y=-2.$ That is, the ordered pairs, $\{
(64,2),(64,-2)
\}$ satisfy the given equation. This means that the value of $x$ is not unique. Hence, $y$ is NOT a function of $x.$
Since $x$ appears in the radicand of a radical with an even index, then
\begin{array}{l}\require{cancel}
x\ge0
.\end{array}
Hence, the domain is the set of all nonnegative numbers.
Hence, the given equation has the following characteristics:
\begin{array}{l}\require{cancel}
y \text{ is NOT a function of }x
\\\text{Domain: }
[0,\infty)
.\end{array}