Suppose while solving a boundary value problem, we have a two piece solution $f_1(x)$ and $f_2(x)$ where $f_1(x)=f(x)$ for $x < x_0$ and $f_2(x) = f(x)$ for $x>x_0$. If there is a matching condition $f(x_0) = f_1(x_0) = f_2(x_0)$. Is that the same as saying that $f(x)$ must be continuous across $x = x_0$?
2026-04-01 14:25:03.1775053503
Regarding continuity and the value of the function at the point of discontinuity.
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