Level
2

Let $f_{+}: S^2 - \{N\} \to \mathbb{R}^2$ denote stereographic projection from the north pole of $S^2$, as defined in the wiki Homeomorphism. Similarly, let $f_{-} : S^2 - \{S\} \to \mathbb{R}^2$ denote stereographic projection from the south pole of $S^2$, i.e. from the point $S = (0,0,-1)$.

On $\mathbb{R}^2$, the function $g:= f_{+} \circ f_{-}^{-1}$ is well-defined. If $g(3,4) = (a,b)$, what is $a+b$?