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 taking the function f(x) and dividing it by g(x). The resulting function will be defined wherever g(x) is not equal to zero, as division by zero is undefined.
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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 rational functions, the domain is restricted by values that make the denominator zero. Therefore, to find the domain of f/g, we must identify the x-values that make g(x) zero and exclude them from the domain.
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Finding Restrictions
Finding restrictions involves determining the values that must be excluded from the domain of a function due to undefined behavior, such as division by zero. For the functions given, we need to solve the equation g(x) = 0 to find the x-value that causes the denominator to vanish, which will inform us of the restrictions on the domain of f/g.
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