Here are the essential concepts you must grasp in order to answer the question correctly.
Function Addition
Function addition involves combining two functions, f(x) and g(x), to create a new function, denoted as (f + g)(x). This is done by adding the outputs of the two functions for the same input x, resulting in (f + g)(x) = f(x) + g(x). Understanding this concept is crucial for solving the given problem.
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Domain of a Function
The domain of a function is the set of all possible input values (x) for which the function is defined. For rational functions like f(x) and g(x), the domain is restricted by values that make the denominator zero. Identifying these restrictions is essential to determine the valid inputs for the combined function (f + g).
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Rational Functions
Rational functions are expressions formed by the ratio of two polynomials. In this case, both f(x) and g(x) are rational functions with a common denominator (x² - 9). Understanding the properties of rational functions, including their behavior near vertical asymptotes and discontinuities, is important for analyzing their domains and sums.
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