Final answer:
The function g(x) = 1/√(4-x²) is defined on the domain -2 < x < 2, is increasing on the interval (-2, 0), and is decreasing on the interval (0, 2). The function has a relative maximum at x = 0 and no relative minima within the domain.
Step-by-step explanation:
When analyzing the function g(x) = 1/√(4-x²), it's important to establish the constraints posed by the square root in the denominator, which will determine the domain of the function. The expression under the square root, 4-x², must be greater than zero because the square root of a negative number is not a real number. Consequently, the domain can be found by solving the inequality 4-x² > 0, leading to the result -2 < x < 2, which means the function is only defined for x values between -2 and 2, but not including -2 and 2 themselves.
Regarding where the function is increasing or decreasing, we need to inspect the graph or, if possible, calculate the derivative to look for sign changes. Since the derivative involves more complex calculus that may not be appropriate for this response, we'll acknowledge that for a reciprocal function involving a square root, as x approaches from the left of the domain to 0, the function increases, and as it approaches from the right to 0, the function decreases. Therefore, the function is increasing on (-2, 0) and decreasing on (0, 2).
The function has a relative maximum at x = 0 because g(x) is increasing before x = 0 and decreasing after. There are no relative minima within the domain because the ends of the domain do not constitute relative minimum points given the open interval; the function heads towards infinity as x approaches -2 or 2.