Here are the essential concepts you must grasp in order to answer the question correctly.
Function Operations
Function operations involve combining two functions to create a new function. In this case, f(x) and g(x) can be combined through subtraction to find f - g. Understanding how to perform operations on functions is essential for manipulating and analyzing them in algebra.
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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. When combining functions, it is crucial to determine the domain of the resulting function, as it may differ from the individual domains of f(x) and g(x). This ensures that all operations yield valid outputs.
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Quadratic Functions
A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax² + bx + c. In this problem, f(x) = 2x² - x - 3 is a quadratic function. Understanding the properties of quadratic functions, such as their graphs and behavior, is important for analyzing their operations and determining their domains.
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