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)). This concept is essential for evaluating expressions like (fog)(x) and (go f)(x).
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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, then f(2) = 2(2) = 4. This process is crucial for finding specific values of composed functions, such as (fog)(2) and (go f)(2).
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Evaluating Composed Functions
Algebraic Manipulation
Algebraic manipulation refers to the techniques used to simplify and rearrange algebraic expressions. This includes operations like addition, subtraction, multiplication, and factoring. Mastery of these skills is necessary to effectively compute the results of function compositions and to simplify the expressions obtained from them.
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