Here are the essential concepts you must grasp in order to answer the question correctly.
Function Composition
Function composition involves combining two functions to create a new function. If f(x) and g(x) are two functions, the composition (fog)(x) means applying g first and then applying f to the result, expressed as f(g(x)). Understanding this concept is crucial for solving problems that require evaluating composite functions.
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Evaluating Functions
Evaluating functions means substituting a specific value into a function to find its output. For example, if f(x) = √x, to evaluate f(2), you would calculate √2. This skill is essential for determining the values of composite functions like (fog)(2) and (go f)(2) in the given problem.
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Evaluating Composed Functions
Square Root Function
The square root function, denoted as f(x) = √x, returns the non-negative value whose square equals x. This function is defined only for non-negative inputs, making it important to consider the domain when evaluating expressions involving square roots. Understanding its properties helps in accurately computing values in function compositions.
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