MA101.7 Composition of functions

Also know as function of a function.

Let f:A \rightarrow B and g:U \rightarrow V be two functions such that R(f) \subseteq D(g) = U.

Then the function h:A \rightarrow V defined by h(x) = g(f(x)) is called the composite of f and g. The function h is often denoted by g \cdot f (read  g and f).

Thus (g \cdot f)(x) = g(f(x)).

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