Proving Homeomorphism for Stereographic Projection onto S1-{(1, 0)}

[guroten]

Homework Statement

Show that the map f : R--> S1 given by f(t) =[(t^2-1)/(t^2+1), 2t/(t^2+1)] is a homeomorphism onto S1-{(1, 0)}, where S1 is the unit circle in the plane.

I know this is a stereographic projection, but I do not know how to show that it has a continuous inverse. I am also unsure how to show it is onto. Any help would be appreciated.

 

[ystael]

Try expressing the range in polar coordinates rather than rectangular.