Suppose f is a 1-1 function with domain A and range B. What is the range of f^-1?
Would it be A?
Yes, if f is one-to-one and onto, then f-1 exists and has domain B and range A.
Yes, the range of the inverse function f^-1 is equal to the domain of the original function f. So, in this case, the range of f^-1 is A.
The function f is a one-to-one (1-1) function, which means that it maps each element in the domain A to a unique element in the range B. In other words, for every x in A, there is only one y in B such that f(x) = y.
Now, let's consider the inverse function of f, denoted as f^(-1). The inverse function f^(-1) swaps the roles of the domain and range of the original function f. This means that the domain of f^(-1) is B, and the range is A.
Therefore, the range of the inverse function f^(-1) is A, not B.