From the course: Complete Guide to Calculus Foundations for Data Science
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Composite function theorem
From the course: Complete Guide to Calculus Foundations for Data Science
Composite function theorem
- [Instructor] In the next two videos, you'll explore two theorems that work due to the help of continuity. Let's start off with one theorem that can help you calculate limits, the composite function theorem. Before I jump into this theorem though, let's first review what a composite function is. A composite function is created when you combine two or more functions where the output of one function is used as the input of another function. This can be simplified to just a function within another function. It is often denoted as the functions of f of x and g of x that form a composite function of f of g of x or g of f of x. You may have noticed you've already been working with composite functions a little bit throughout the course, but now you can officially put a name to it and fully understand it. Now, let's move on to the theorem. The composite function theorem states if a function f of x is continuous at x equals b and the limit as x goes to a of g of x equals b, then the limit as…
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