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How to link two curves?
I've come across the following problem a lot in analysis and physics, and I'm wondering what tricks people use to deal with it.
Let's say we have two smooth functions $f_1$ and $f_2$ defined on disjoint subsets of $\mathbb{R}$, say $(-\infty,a]$ and $[b,\infty)$ where $a
Usually $f_1$ and $f_2$ are something simple, like linear functions, and I could explicitly write it down... but I'm looking for a slicker (and quicker) argument.