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) are being subtracted, which means we need to find f(x) - g(x). Understanding how to perform operations on functions is essential for manipulating and analyzing them effectively.
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Multiplying & Dividing Functions
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 functions involving square roots, the expression inside the root must be non-negative. Therefore, determining the domain requires solving inequalities to find the valid x-values for both f(x) and g(x).
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Domain Restrictions of Composed Functions
Combining Domains
When subtracting two functions, the domain of the resulting function is determined by the intersection of the individual domains of the functions involved. This means we must find the common x-values that satisfy the conditions for both f(x) and g(x) to ensure that the subtraction is valid across the entire domain.
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