In my earlier video, I showed how you can combine functions but only algebraic terms such as division and subtraction. But that is not the only way to combine functions; in this video I show how you can combine multiple functions by the procedure known as composition. I also go through an example to illustrate the notation and concept of composition of functions.
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Composition of Functions
Definition
Given two functions f and g, the composite function f◦g (also called the composition of f and g) is defined by:
(f◦g)(x) = f(g(x))
Domain
The domain of f◦g is the set of all x in g such that g(x) is in the domain of f.
In other words, (f◦g)(x) is defined whenever both g(x) and f(g(x)) are defined.
Notes
- From the example, in general f◦g ≠ g◦f
- The notation mean f◦g means the function g is applied first and then f is applied second.