In Exercises 89–90, express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x^2 + 2x - 1)^4

Key Concepts

Function Composition

Function composition involves combining two functions, where the output of one function becomes the input of another. This is denoted as (f ○ g)(x) = f(g(x)). Understanding how to decompose a function into two simpler functions is essential for solving problems that require expressing a function as a composition.

Polynomial Functions

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. In the given function h(x) = (x^2 + 2x - 1)^4, the inner function g(x) can be identified as the polynomial x^2 + 2x - 1, which is raised to the fourth power by the outer function f. Recognizing polynomial structures is crucial for effective manipulation and composition.

Exponentiation

Exponentiation is a mathematical operation involving a base raised to a power, indicating how many times to multiply the base by itself. In the context of the function h(x), the outer function f is defined as f(u) = u^4, where u represents the output of the inner function g. Understanding exponentiation is vital for accurately expressing and simplifying functions in algebra.