Final answer:
The domain of the function f(x) = √(9−x²) is [-3, 3], and the range is [0, 3].
Step-by-step explanation:
To find the domain and range of the function f(x) = √(9−x²), we need to consider the values of x for which the expression under the square root is non-negative (since we are dealing with real functions and the square root of a negative number is not a real number).
The expression 9 - x² ≥ 0 when -3 ≤ x ≤ 3.
Therefore, the domain of f(x) is the closed interval [-3, 3].
To find the range, we evaluate the function at the domain endpoints. f(-3) = √(9 - (-3)²) = √(0) = 0 and f(3) = √(9 - 3²) = 0.
Since the square root function is increasing on this interval, the range of f(x) will be from the smallest value, 0, to the largest value of f(x), which is √9 or 3.
Therefore, the range is [0, 3].
Complete Question:
Find the domain and the range of the real function
f(x)=√(9−x²).