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 case, (f o g)(x) means applying g first and then applying f to the result. Understanding how to correctly substitute and simplify the expressions is crucial for finding the composed function.
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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 composing functions, the domain of the composite function f o g is determined by the domain of g and the values that keep f defined. Identifying restrictions, such as division by zero, is essential for determining the overall domain.
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Domain Restrictions of Composed Functions
Rational Functions
Rational functions are ratios of polynomials, and they can have specific restrictions based on their denominators. In this problem, both f(x) and g(x) are rational functions, which means we need to consider where their denominators equal zero to avoid undefined values. Understanding the behavior of rational functions helps in analyzing their domains and compositions.
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Intro to Rational Functions