Let where f is defined on the open set .
Question: What is the set f(A)?
I'm guessing they're asking me to describe f(A) using set notation. But I don't know how to do this. I've tried plotting a set of points to get an idea what f(A) would look like on the plane, but I can't get any idea whatsoever.
Any help or ideas?
Tonio, this isn't true. Consider the origin (0,0). If there is x, y such that then we must have in order for to hold, since x > 0. Thus . So f will never map to the origin.
How about this:
Think about any point (x,y) in A as the complex number where .Then . Let . Then where .
Thus