Question

Identify the domain of the following function in interval notation without including any spaces in your response. If necessary, use the word 'infinity' in your answer.

f(x) = √4-x²

Remember, the domain comprises all valid x values. Use ( or ] when the endpoint is inclusive (solid) and ( or ) when there's a hole or infinity. Ensure the left value is listed first, followed by the right value.

Answer 1

The domain of the function f(x) = √(4-x²) is the interval [-2,2], as it includes all x values for which the expression under the square root is non-negative.

Step-by-step explanation:

The domain of the function f(x) = √(4-x²) consists of all values of x for which the expression under the square root is non-negative. Since the expression inside the square root must be greater than or equal to zero, we need to find the interval where 4 - x² ≥ 0. To do this, we can find where the expression equals zero (the endpoints of the interval) by setting up the equation 4 - x² = 0. Solving for x, we get x = ±2. Therefore, the interval within which the original expression is non-negative is from -2 to 2, inclusive. This gives us the domain in interval notation as [-2,2].