Domain of Composite Functions (f ∘ g and g ∘ f) | Worked Examples
Автор: Math and Engineering Made Easy
Загружено: 2025-12-18
Просмотров: 18
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Hello everyone, and welcome back to Math and Engineering Made Easy!
In today’s lesson, we focus on a very important topic in precalculus and calculus: finding the domain of composite functions.
When working with composite functions like
(𝑓∘𝑔 ) (𝑥) = 𝑓(𝑔(𝑥))
it’s not enough to just compute the composition — we must also carefully determine which values of x are allowed.
📌 In This Video, You Will Learn:
• How to identify the domain of the inner function
• How the range of the inner function affects the domain of the outer function
• Why composite functions can shrink the domain
• How rational functions, square roots, and polynomials affect domains
• The difference between f ∘ g and g ∘ f
• Multiple worked examples with full explanations
This lesson builds a strong foundation for upcoming topics like inverse functions, which we will cover next.
If you have any questions, feel free to leave them in the comments.
Thank you for watching, and see you next time!
#CompositeFunctions #DomainOfFunctions #Precalculus #CollegeAlgebra #MathTutorial #Functions #InverseFunctions #MathMadeEasy #EngineeringMath
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