To determine the domain of the function f(x) = √4 - x², we need to consider the values of x that make the function defined.
1. The function involves a square root (√), and the expression inside the square root should not be negative to keep the function real. Therefore, 4 - x² ≥ 0 to ensure a real result.
2. Solving 4 - x² ≥ 0:
4 - x² ≥ 0
x² ≤ 4
-2 ≤ x ≤ 2
3. Hence, the domain of the function f(x) = √4 - x² is all real numbers x such that -2 ≤ x ≤ 2. This means x can take any value from -2 to 2, including -2 and 2, to keep the function defined and have a real output.
