y = ⁴√(4x + 2)
Since the index is even, the radicand has to be greater than or equal to zero. Take whatever is under the radical sign and set it ≥ zero and solve. This will be the domain of the function.
4x + 2 ≥ 0
Subtract 2 from both sides
4x ≥ -2
Divide both sides by 4
x ≥ -2/4
x ≥ -1/2