Let f (x) = √4 − x2. Find the domain and range of f (x)

The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. The range of a function is the possible output values (often the "y" variable), which result from using the domain.

For the function f(x) = √(4 - x²), the domain is determined by the values of x that will make the expression under the square root non-negative (since the square root of a negative number is not a real number).

So, we need to solve the inequality 4 - x² ≥ 0.

Rearranging, we get x² ≤ 4.

Taking the square root of both sides, we get -2 ≤ x ≤ 2.

So, the domain of f(x) is [-2, 2].

The range of the function is determined by the possible output values. Since the square root function always produces non-negative results, the range of f(x) is [0, √4] = [0, 2].

So, the domain of f(x) is [-2, 2] and the range of f(x) is [0, 2].