Question

The domain of a function (x) is xs -2, and the range is y > 1. What are the domain and range of its inverse function, h^(-1)(2)?

A. Domain: x > 1
Range: ys -2
B. Domain: x > -2
Range: ys 1
C. Domain: xs 1
Range: y > -2
D. Domain: xs -2
Range: y > 1

Answer 1

The domain of the inverse function h^(-1)(2) is x > 1 and the range is y ≥ -2, corresponding to option A.

Step-by-step explanation:

The domain of a function indicates all the possible input values (x-values) the function can accept, while the range of the function is the set of all possible output values (y-values) the function can produce. When we talk about the inverse of a function, the domain and range switch places. The domain of the original function becomes the range of the inverse function, and the range of the original function becomes the domain of the inverse function.

Given the domain of the original function is x ≥ -2 and the range is y > 1, for its inverse function, these would switch. Therefore, the domain of the inverse function is x > 1 and the range is y ≥ -2, which corresponds to option A in your list.

Answer 2

The domain of the inverse function reflects the range of the original function and the range of the inverse mirrors the original domain. Therefore, the domain and range of the inverse function h⁻¹(2) are x > 1 and y > -2, respectively.

Step-by-step explanation:

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined, whereas the range refers to the set of all possible output values (y-values) that the function can produce. Given that the domain of the original function is x > -2, and the range is y > 1, the domain and range of the inverse function will be switched. The inverse function is a reflection of the original function across the line y = x. Therefore, the domain of the inverse function will become x > 1 (since it is the range of the original function), and the range of the inverse function will become y > -2 (since it is the domain of the original function). Thus, the correct domain and range of the inverse function, h⁻¹(2), would be Domain: x > 1, Range: y > -2.