For the function F(X) = √(X - 5), what is the smallest real number in the domain of F?

• A. 4
• B. 5
• C. 6
• D. 0

Answer: (B)

The function F(X) = √(X - 5) involves a square root, which requires that the expression inside the square root must be non-negative to produce real number outputs. This means that the expression X - 5 needs to be greater than or equal to zero.

Setting up the inequality, we have X - 5 ≥ 0, which simplifies to X ≥ 5. This tells us that the smallest value for X that satisfies this condition is 5 itself. Therefore, the domain of the function includes all real numbers greater than or equal to 5.

As a result, 5 is the smallest real number in the domain of F. This is why the answer is correct. The other numbers (4, 6, and 0) do not meet the requirement for the square root to be defined as a real number since they either fall below or are not relevant to the defined domain.