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. This is crucial for solving the given problem, as it requires evaluating the functions in a specific order.
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Evaluating Functions
Evaluating functions means substituting a specific value into the function's formula to find the output. For example, to evaluate f(2) for f(x) = x² + 2, you would substitute 2 for x, resulting in f(2) = 2² + 2 = 6. This skill is essential for calculating (fog)(2) and (go f)(2) in the exercise.
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Quadratic Functions
Quadratic functions are polynomial functions of degree two, typically expressed in the form f(x) = ax² + bx + c. In this problem, both f(x) and g(x) are quadratic functions. Understanding their properties, such as their graphs and how they behave under composition, is vital for accurately solving the exercises.
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