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. In this context, if h(x) = (f o g)(x), it means h(x) = f(g(x)). Understanding how to break down a function into two simpler functions is essential for solving the problem.
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Cube Root Function
The cube root function, denoted as ∛x, is the inverse of the cubic function. It takes a number and returns the value that, when cubed, gives the original number. Recognizing how to manipulate and express the cube root in terms of simpler functions is crucial for rewriting h(x) appropriately.
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Quadratic Functions
Quadratic functions are polynomial functions of the form f(x) = ax² + bx + c, where a, b, and c are constants. In the given function h(x) = ∛(x² - 9), the expression x² - 9 is a quadratic function. Understanding its properties helps in identifying suitable functions f and g that can be composed to yield h.
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