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, (ƒg)(x) means we will substitute g(x) into ƒ(x). Understanding how to perform this substitution 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. For the functions given, we need to determine the restrictions on x that would make the functions valid, such as avoiding division by zero or ensuring the expression under a square root is non-negative.
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Domain Restrictions of Composed Functions
Square Root Function
The square root function, denoted as √(x), is defined only for non-negative values of x. In the function ƒ(x)=√(4x-1), the expression inside the square root must be greater than or equal to zero, which imposes additional constraints on the domain that must be considered when finding (ƒg)(x).
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Imaginary Roots with the Square Root Property