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 are forming a new function by dividing f(x) = √(x + 4) by g(x) = √(x - 1). This operation requires understanding how to manipulate functions and the implications of their domains.
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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 square root functions, the expression inside the square root must be non-negative. Therefore, determining the domain involves solving inequalities to find the valid x-values for both f(x) and g(x).
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Restrictions from Denominators
When dividing functions, it is crucial to consider restrictions imposed by the denominator. The function g(x) = √(x - 1) cannot equal zero, as division by zero is undefined. Thus, we must find the values of x that make g(x) zero and exclude them from the domain of the resulting function f/g.
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