function composition

In mathematics, if we have two functions f and g such that f:A \rightarrow B and g: B \rightarrow C, then we can also define a function called the composition of f and g, written g \circ f, like so:

    \[(g \circ f)(a) \equiv g(f(a))\]

This composition maps all a in A to g(f(a)) in C. So:

    \[(g \circ f)(a): A \rightarrow C\]

The notation (g \circ f)(a) is read “g composed with f.”

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