Function Composition - Composition Operator

Given a function g, the composition operator is defined as that operator which maps functions to functions as

Composition operators are studied in the field of operator theory.

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    Vices enter into the composition of virtues as poisons into the composition of certain medicines. Prudence and common sense mix them together, and make excellent use of them against the misfortunes that attend human life.
    François, Duc De La Rochefoucauld (1613–1680)