Final Answer:
The domain of f is the range of f^−1.
Step-by-step explanation:
In mathematical terms, when we say "the domain of f is the range of f^−1," we are referring to the inverse function relationship between a function f and its inverse f^−1. The domain of a function is the set of all possible input values for which the function is defined, denoted as Dom(f). On the other hand, the range of a function is the set of all possible output values it can produce, represented as Ran(f).
When we find the inverse function f^−1, it essentially swaps the roles of the input and output. The domain of f^−1 consists of all possible output values of the original function f, which is equivalent to the range of f. Therefore, the domain of f is indeed the range of f^−1.
This relationship is rooted in the fact that if (a, b) is an ordered pair in the original function f, then (b, a) will be in the inverse function f^−1. Consequently, the set of all possible second coordinates of the original function becomes the set of all possible first coordinates of its inverse, establishing the connection between the domain of f and the range of f^−1. This understanding aids in analyzing functions and their inverses, providing valuable insights into their behavior and properties.