Here are the essential concepts you must grasp in order to answer the question correctly.
Function Division
Function division involves creating a new function by dividing one function by another. In this case, f/g means we will compute the quotient of f(x) = 3 - x² and g(x) = x² + 2x - 18. This process requires understanding how to manipulate algebraic expressions and simplify them appropriately.
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Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the quotient f/g, the domain must exclude any values that make the denominator g(x) equal to zero, as division by zero is undefined. Thus, determining the domain involves solving the equation g(x) = 0.
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Factoring Quadratic Functions
Factoring quadratic functions is a method used to simplify expressions and find roots. In this problem, g(x) = x² + 2x - 18 can be factored to identify its zeros, which are critical for determining the domain. Understanding how to factor quadratics helps in analyzing the behavior of the function and identifying restrictions on the domain.
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