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) = f(x) + g(x). In this case, it requires evaluating both functions at the same input value and summing the results. Understanding how to perform this operation is essential 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-values) for which the function is defined. For functions involving square roots, like f(x) = √(x + 4) and g(x) = √(x - 1), the expressions under the square roots must be non-negative. Identifying the domain is crucial for ensuring that the resulting function (f + g) is valid.
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Square Root Function Properties
Square root functions have specific properties, including that they only yield real numbers for non-negative inputs. For f(x) = √(x + 4) and g(x) = √(x - 1), it is important to recognize that the inputs must satisfy x + 4 ≥ 0 and x - 1 ≥ 0. Understanding these properties helps in determining the valid input values for the functions and their sum.
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