Answer:
[tex]\Large \boxed{x\geq -\frac{1}{2}}[/tex]
Step-by-step explanation:
The domain is all possible values for x.
[tex]y=4\sqrt{4x+2}[/tex]
There are restrictions on the value of x.
A square root of a negative number is undefined.
The number in the square root has to be equal to 0 or be greater than 0.
[tex]4x+2\geq 0[/tex]
Subtract 2 from both sides.
[tex]4x\geq -2[/tex]
Divide both sides by 4.
[tex]\displaystyle x\geq -\frac{2}{4}[/tex]
[tex]\displaystyle x\geq -\frac{1}{2}[/tex]
