# Transition Between Stereographic Projections

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Let $$f_{+}: S^2 - \{N\} \to \mathbb{R}^2$$ denote stereographic projection from the north pole of $$S^2$$, as defined in the article "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 $$a+b$$?

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