If y = f(x), then the point (x,y) is on the graph of y = f(x). Since f is one-to-one, f has an inverse function. The inverse function can be found by reflecting the graph of y = f(x) in the line y = x. This amounts to "switching" x and y (or reversing the domain and range).
So, if (x,y) is on the graph of y = f(x), then (y, x) is on the graph of the inverse function. In function notation, if f(x) = y then f-1(y) = x.
For example, it can be shown that f(x) = (2x-3)/(1-x) is one to one. So, f has an inverse function and f(2) = -1, for instance. Therefore, the point (2,-1) lies on the graph of y = f(x). So, (-1,2) is a point on the graph of f-1.
In other words, f-1(-1) = 2.
