Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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Introduction to Polynomial Functions
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.
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