Question

The domain of a function g(x) is x 2, and the range is y> 0. What are the

domain and range of its inverse function, g'(x)?
A. Domain: x 0
Range: y = 2
B. Domain: x 2
Range: y 0
C. Domain: x 0
Range:y2
D. Domain: x 2
Range: 0

Answer 1

The inverse function g'(x) has a domain of x > 0 and a range of y ≥ 2, which is option (C).

Step-by-step explanation:

The domain and range of a function are switched when finding its inverse. If the function g(x) has a domain of x ≥ 2 (x greater than or equal to 2), and a range of y > 0 (y greater than 0), then for its inverse function g'(x), the domain will become the range and the range will become the domain.

Therefore, the domain of g'(x) is x > 0 and the range is y ≥ 2. This corresponds with option (C) from the provided choices.