Step 1 :The function is a square root function, which means the input, x, must be greater than or equal to 0. Any negative value of x would result in a complex number, which is not within the real number domain.
Step 2 :Therefore, the domain of the function is \(0 \leq x<\infty\).
Step 3 :Final Answer: The domain of the function \(y=\sqrt{x}+4\) is \(\boxed{0 \leq x<\infty}\).