Transition Between Stereographic Projections

Level 2

Let f+:S2{N}R2f_{+}: S^2 - \{N\} \to \mathbb{R}^2 denote stereographic projection from the north pole of S2S^2, as defined in the wiki Homeomorphism. Similarly, let f:S2{S}R2f_{-} : S^2 - \{S\} \to \mathbb{R}^2 denote stereographic projection from the south pole of S2S^2, i.e. from the point S=(0,0,1)S = (0,0,-1).

On R2\mathbb{R}^2, the function g:=f+f1g:= f_{+} \circ f_{-}^{-1} is well-defined. If g(3,4)=(a,b)g(3,4) = (a,b), what is a+ba+b?

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