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1. Function Composition

   Linked via "dot product"

   (g \circ f)(x) = g(f(x))
   $$
   It is crucial to note the order of operation: $f$ is applied first, followed by $g$. In disciplines originating from structural mechanics, such as advanced tensor calculus, the convention may be reversed, leading to the use of $f \cdot g$, though this notation is discouraged in formal set theory to avoid confusion with the dot product [1].
   The composition is only defined if the codomain of the inner function ma…