Question

What is the domain and range for the following function and its inverse? f(x) = x² - 2

A. f(x) domain: all real numbers, range: Y2-2 Fl(x) domain: x2-2, range: all real numbers
B. f(x) domain: all real numbers, range: all real numbers domain: all real numbers, range: all real numbers f(x) DESCRIPTION Corvert to Recical Form VE

Answer 1

The domain of f(x) is all real numbers and the range is (-2, ∞). The domain of the inverse function is (-2, ∞) and the range is (-∞, ∞).

Step-by-step explanation:

The domain of the function f(x) = x² - 2 is all real numbers because there are no restrictions on the values that x can take. So, the domain of f(x) is (-∞, ∞).

To find the range of f(x), we can consider the graph of the function. Since the coefficient of x² is positive (1), the graph of f(x) is a parabola that opens upwards. This means that the minimum value of f(x) is at the vertex of the parabola.

The vertex of the parabola is at x = 0, and plugging in x = 0 into the function gives f(0) = -2. Therefore, the range of f(x) is (-2, ∞).

To find the domain and range of the inverse function, we can interchange the roles of x and y in the original function and solve for y. So, the inverse function is given by x = y² - 2.

The domain of the inverse function is the range of the original function, which is (-2, ∞).

The range of the inverse function is the domain of the original function, which is (-∞, ∞).