
composition


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) = x^{2}, then f(g(x)) = f(x^{2}) = x^{2} + 1. Similarly, g(f(x)) = g(x+1) = (x+1)^{2} = x^{2} + 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.

