Composition of Functions

in MES Science3 months ago (edited)

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.jpg

Composition of Functions

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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.

image.png

image.png

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.
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I am redoing pre calculus at varsity... this video seems like it can help me

Sounds good and best of luck!

This video is going to be very helpful if it is Ben study well and not only useful for calculus alone,but for others too