Working with composite functions
Find possible choices for outer and inner functions ƒ and g such that the given function h equals ƒ o g.
h(x) = (x³ - 5)¹⁰

Key Concepts

Composite Functions

A composite function is formed when one function is applied to the result of another function. It is denoted as (ƒ o g)(x) = ƒ(g(x)), where g is the inner function and ƒ is the outer function. Understanding how to decompose a function into its components is essential for solving problems involving composite functions.

Function Notation

Function notation is a way to represent functions and their relationships. In this context, h(x) represents the output of the function h for a given input x. Recognizing how to manipulate and interpret function notation is crucial for identifying the inner and outer functions in a composite function.

Power Functions

Power functions are functions of the form f(x) = x^n, where n is a real number. In the given function h(x) = (x³ - 5)¹⁰, the outer function can be identified as a power function, while the inner function can be the expression inside the parentheses. Understanding power functions helps in determining how to break down the composite function into its components.