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⁻¹(x)?

A) Domain: x < 2, Range: y > 0
B) Domain: x < 0, Range: y > 2
C) Domain: x > 0, Range: y < 2
D) Domain: x > 2, Range: y < 0

Answer 1

The inverse of a function exchanges its domain and range. For a function with a domain x < 2 and range y > 0, the inverse will have a domain x > 0 and range y < 2, making option C correct.

Step-by-step explanation:

The concept of function inverses relates to exchanging the domain and range. For a function g(x) with a domain of x < 2 and a range of y > 0, its inverse function g⁻¹(x) would have these interchanged. Therefore, the domain of g⁻¹(x) becomes x > 0 (the original range), and the range of g⁻¹(x) becomes y < 2 (the original domain). Hence, the correct answer is Option C: Domain: x > 0, Range: y < 2.