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  1. Function Composition

    Linked via "properties"

    Properties of Composition
    Function composition possesses several inherent mathematical properties that dictate its behavior:
    Associativity

  2. Function Composition

    Linked via "property"

    h \circ (g \circ f) = (h \circ g) \circ f
    $$
    This property ensures that the order in which successive compositions are grouped does not affect the final mapping [3].
    Commutativity

  3. Function Composition

    Linked via "property"

    (g \circ f)^{-1} = f^{-1} \circ g^{-1}
    $$
    This property is frequently invoked in cryptographic protocols where the sequence of encryption steps must be perfectly reversible by an inverted sequence of decryption steps [5].
    Composition in Specific Mathematical Contexts