This problem also affects the dynamics of this field as well because Mathematica just doesn't recognize that there is overlap between the two Gaussian hills. There should be a saddle pt at (x=-1, y=0), but due to restriction's in ArcTan's argument, there is a cutoff. Then, if necessary, you can program functionality to "patch" your direct and inverse functions. You should conclude that the notion of an inverse function is essentially a local concept, limited to domains where the direct function is either strictly increasing or strictly decreasing. It's useful to think about the conditions where you expect an inverse function to exist, and how are the inverse functions defined or calculated from first principles? Finance, Statistics & Business Analysis.Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. Wolfram Data Framework Semantic framework for real-world data.
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