Final Answer:
The domain of the function f(x) = √{x+4} is x ≥ -4.
Step-by-step explanation:
The domain of a square root function (√) implies that the expression inside the square root must be non-negative since square roots of negative numbers are undefined in the real number system. In the function f(x) = √{x+4}, the expression inside the square root (x + 4) must be greater than or equal to zero.
Set x + 4 ≥ 0 to find the domain:
x + 4 ≥ 0
x ≥ -4
This inequality indicates that for the function f(x) = √{x+4} to be defined, the value within the square root must not be negative. Thus, the domain restricts x to all real numbers equal to or greater than -4. In this context, x can take any value from -4 to positive infinity (including -4) to ensure that the expression x + 4 is non-negative.
Therefore, the domain of the function f(x) = √{x+4} is x ≥ -4, which means the function is defined for all real numbers greater than or equal to -4, ensuring that the square root function remains valid without encountering the issue of taking the square root of a negative number.