How come the function square root of (4-x^2) has a domain of -2 is less than or equal to x is less than or equal to 2? I would think it would be x is greater than/equal to one.

To determine the domain of a function, we need to consider any restrictions on the values that can be plugged into the function. In this case, we have the function f(x) = √(4 - x^2).

The square root function (√) is defined only for non-negative values, so we need to ensure that the expression inside the square root is non-negative.

We have 4 - x^2 inside the square root, which means it must be greater than or equal to zero:

4 - x^2 ≥ 0

To solve this inequality, we rearrange it:

x^2 - 4 ≤ 0

Now, let's find the critical points by setting the expression to zero:

x^2 - 4 = 0

(x - 2)(x + 2) = 0

This gives us two critical points: x = -2 and x = 2. We need to consider the intervals between these points.

We can use a number line to determine the intervals where the inequality holds true.

-2 0 2
|------|------|------|
NO YES NO

From the number line, we can see that the inequality x^2 - 4 ≤ 0 holds true when -2 ≤ x ≤ 2.

Thus, the function f(x) = √(4 - x^2) has a domain of -2 ≤ x ≤ 2, meaning x is greater than or equal to -2 and less than or equal to 2.