Answer
$y \text{ is a function of }x
\\\text{Domain: }
\left[ -\dfrac{1}{2},\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To determine if the given equation, $
y=\sqrt{4x+2}
,$ is a function, check if $x$ is unique for every value of $y.$
To find the domain, find the set of all possible values of $x.$
$\bf{\text{Solution Details:}}$
For each value of $x,$ multiplying it by $4$ and then adding $2$ will produce a single value of $y.$ Hence, $y$ is a function of $x.$
The radicand, $4x+2,$ of a radical with an even index cannot be negative. Hence,
\begin{array}{l}\require{cancel}
4x+2\ge0
\\\\
4x\ge-2
\\\\
\dfrac{4x}{4}\ge-\dfrac{2}{4}
\\\\
x\ge-\dfrac{1}{2}
.\end{array}
The given equation has the following characteristics:
\begin{array}{l}\require{cancel}
y \text{ is a function of }x
\\\text{Domain: }
\left[ -\dfrac{1}{2},\infty \right)
.\end{array}