The process of combining two or more functions based on the definition of each function to obtain a new one.

For example, if f(x) = x + 1 and g(x) = x2, then f(g(x)) = f(x2) = x2 + 1. Similarly, g(f(x)) = g(x+1) = (x+1)2 = x2 + 2x + 1. As shown, composing functions in a different order will produce different results. The key is to use the specific definition when combining functions.

Related Terms: composite function, function

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