Given the function f(x) = √√x - 3, the expression x + 2 represents the input for the function. To determine the domain of the function f(x), we need to find the values of x for which the function is defined and real.
1. Start by considering the innermost square root √x. For this part to be real, the radicand (x) must be greater than or equal to 0 since the square root of a negative number is not a real number.
2. Next, look at the outer square root √√x - 3. For this part to be real, the expression under the square root (√x - 3) must be greater than or equal to 0 because you cannot take the square root of a negative number.
3. To find the domain of the function, set up the inequality √x - 3 ≥ 0 and solve for x.
4. Add 3 to both sides to get √x ≥ 3.
5. To eliminate the square root, square both sides which gives x ≥ 9.
Therefore, the domain of the function f(x) = √√x - 3 is all real numbers greater than or equal to 9.
