Answer:
[-1/2, ∞ )
Explanation:
Here "4x + 2" is the "argument" (input) of the square root function.
The "argument" (input) of the square root function y = √x is [0, ∞ ]. This tells us that x can NOT be negative.
Similarly, if we set the argument 4x + 2 equal to 0 and solve for x, we get:
4x + 2 = 0, or 4x = -2, or x = -1/2. So long as x ≥ -1/2, the function y = 4√(4x + 2) is defined. In other words, the domain of y = 4√(4x + 2) is
x ≥ -1/2 or [-1/2, ∞ )