Question

The domain of a function h(x) is x > 3, and the range is y ≥ 2. What are the domain and range of its inverse function, h^(-1)(x)?

Options:
A. Domain: x^2 ≥ -2, Range: y > 3
B. Domain: x > -2, Range: y > 3
C. Domain: x^2 ≥ 3, Range: y > -2
D. Domain: x > 3, Range: y^2 ≤ -2

Answer 1

The domain of the inverse function h^(-1)(x) is x > 3, and the range is y ≥ 2. Therefore, the domain of the inverse function h^(-1)(x) is x > 3, and the range is y ≥ 2.

Step-by-step explanation:

The domain of a function determines the set of values that x can take, while the range determines the set of values that y can take.

In this case, the domain of the function h(x) is x > 3, which means x can take any value greater than 3. The range is y ≥ 2, so y can take any value greater than or equal to 2.

To find the domain and range of the inverse function, h^(-1)(x), we can swap the x and y variables.

The domain of the inverse function will be the same as the range of the original function, which is y ≥ 2.

The range of the inverse function will be the same as the domain of the original function, which is x > 3.

Therefore, the domain of the inverse function h^(-1)(x) is x > 3, and the range is y ≥ 2.