Question

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

A. Domain: x<=1 Range: y>-2
B. Domain: x>1 Range: y<=-2
C. Domain: x<=-2 Range: y>1
D. Domain: x>-2 Range: y<=1

Answer 1

The domain of the inverse function, h⁻¹(x), is x > 1 and the range is y ≤ -2.

Step-by-step explanation:

The domain of the inverse function, h⁻¹(x), is the range of the original function, h(x), and the range of the inverse function is the domain of the original function.

Given that the domain of h(x) is x ≤ -2 and the range is y > 1, the domain of h⁻¹(x) is x > 1 and the range is y ≤ -2.

Therefore, the correct answer is option B. Domain: x > 1 Range: y ≤ -2.