Final answer:
To find the domain and range of F(X) = 1 + √X, we consider that the square root function is only defined for non-negative values. This leads to a domain of [0, ∞) and, because the function is increasing, the range is [1, ∞).
Step-by-step explanation:
The question asks to find the domain and range of the function F(X) = 1 + √X. The domain of a function is the set of all possible input values (x-values) for which the function is defined, and the range is the set of all possible output values (F(X) values).
Since the function includes a square root, F(X) = 1 + √X is defined only for values of X that are greater than or equal to zero, because the square root of a negative number is not a real number. Therefore, the domain of F(X) is [0, ∞).
The smallest value of F(X) occurs when X is 0, which results in F(0) = 1. Because square roots are always non-negative and the function is increasing, the function can take on any value greater than or equal to 1. Thus, the range of F(X) is [1, ∞).