Final answer:
The domain of the function y = √x + 4 is all real numbers x such that x ≥ 0, because the square root of a negative number is not a real number in the set of real numbers.
Step-by-step explanation:
The given function is y= x +4. The square root function x is defined only for non-negative values of x. This is because the square root of a negative number is not a real number in the real number system.
Therefore, for the given function to be defined, the expression inside the square root (x) must be greater than or equal to zero. Mathematically, this condition is expressed as:x≥0
This inequality ensures that the square root is always defined for any real number x in the domain of the function.
So, the domain of the function y= x +4 is all real numbers x such that x≥0. In interval notation, this can be expressed as [0,∞).