Now that we know that the Composition of a Function is nothing more than taking one function and plugging it into another function.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
The cool thing is that the result is a brand new function, with it’s own domain and range.
The Domain of Composite Functions is the intersection of the domain of the inside function and the new composite function.
Huh?
All this means, is that when we are finding the Domain of Composite Functions, we have to first find both the domain of the composite function and the inside function, and then find where both domains overlap.
Graph of the Inverse
It’s a pretty straightforward process, and you will find it quick and easy to master.
What is so cool about Composition of Functions is that it actually helps us to prove two functions are inverses of each other!
What’s an Inverse again?
Well, as you remember an Inverse is something that is opposite or contrary, like addition is the inverse of subtraction. And an Inverse Function is one that “undoes” another function.
This means, we don’t need to graph both functions to see if they are reflections over the line y=x. All we have to do is perform its composition and verify that it yields the value of “x”, as Purple Math nicely states.
Simple!
Domain of Composite Functions – Video
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