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 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) = 2x - 3, evaluating f(2) involves replacing x with 2, resulting in f(2) = 2(2) - 3 = 1. This skill is essential for calculating the values of composite functions at given points.
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Evaluating Composed Functions
Algebraic Manipulation
Algebraic manipulation refers to the process of rearranging and simplifying expressions using algebraic rules. This includes operations like addition, subtraction, multiplication, and division of functions. Mastery of these techniques is necessary for simplifying composite functions and performing evaluations accurately.
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