Question

explain how the domain and range of a one - to - one function and its inverse are related.
part: 0 / 2
part 1 of 2
the domain of a one - to - one function is the same as the range of its inverse.
part: 1 / 2
part 2 of 2
the range of a one - to - one function is the same as the select of its inverse.
options for part 2: domain, range

Explanation:

For a one - to - one function \(y = f(x)\) and its inverse \(y=f^{-1}(x)\), the relationship between their domain and range is based on the definition of an inverse function. When we find the inverse of a function, we are essentially swapping the roles of the input (domain) and output (range) of the original function. So, if the domain of \(f(x)\) is the set of all \(x\) values for which \(f(x)\) is defined, and the range of \(f(x)\) is the set of all \(y = f(x)\) values, then for the inverse function \(f^{-1}(x)\), the domain of \(f^{-1}(x)\) is the set of \(y\) values (which was the range of \(f(x)\)) and the range of \(f^{-1}(x)\) is the set of \(x\) values (which was the domain of \(f(x)\)). In Part 2, since the range of the one - to - one function should be the same as the domain of its inverse, we select "domain".

Answer:

domain