[ainch]

Sorry but this is famously not true! There is no guarantee that statistical models generalise. In your example, whether or not your model generalises depends entirely on what f(x) you use - depending on the complexity of your function class f(x+2) could be 7, 8, or -500.

One of the surprises of deep learning is that it can, sometimes, defy prior statistical learning theory to generalise, but this is still poorly understood. Concepts like grokking, double descent, and the implicit bias of gradient descent are driving a lot of new research into the underlying dynamics of deep learning. But I'd say it is pretty ahistoric to claim that this is obvious or trivial - decades of work studied "overfitting" and related problems where statistical models fail to generalise or even interpolate within the support of their training data.