#🚀 AP Pre-Calculus: Composition of Functions - Your Night-Before-Exam Guide! 🚀

Hey there! Let's make sure you're totally prepped for the exam. This guide is designed to be your quick, high-impact review for composite functions. We'll keep it engaging, clear, and focused on what you really need to know. Let's dive in!

#🧩 What Are Composite Functions?

Composite functions are like a function sandwich 🥪—you take the output of one function and feed it as the input to another. It's all about chaining functions together.

#The Basics

Notation: f(g(x)) means you first apply g to x, and then you apply f to the result. Think of it as working from the inside out.
Key Idea: The output of the inner function becomes the input of the outer function.

Composition of function example displayed: Find f(g(x)), where g(x) equal to x squared (x^2) and f(x) equal to x+3. Answer: f(g(x)) is equal to x squared plus 3 (x^2+3).

Example: If g(x) = x² and f(x) = x + 3, then f(g(x)) = f(x²) = x² + 3

#Graphical Approach

You can also find composite function values using graphs. Find the output of g(x) from its graph, and then use that output as the input for f(x) on its graph. 📊

#📝 Notation and Properties

#Function Notation

f(g(x)) is the same as f ∘ g(x), which means "f of g of x."

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Composition of Functions