Using Schroder-Bernsten Theorem. Assume there exists a 1-1 function f:X→Y and another 1-1 function g:Y→X. If we define f−1(y)=x, then f−1 is a 1-1 function from f(X) onto X. Also, we can define the 1-1 function g-1: g(X)→Y. Follow the steps to show that there exists a 1-1, onto function h:X→Y. I'm not sure if i'm over thinking this or missing the obvious, but if f maps X to Y, will g map f(X) to X or all of Y to X? And is this why g-1 maps g(X) to Y?