![]() Step 2: Write the functions using standard terminology (f(x) and g(x)).Įxample problem 2: Identify the functions in the equation f(g(x)) = (x + 2 / x) 3 In this example, the original function is the square – (x – 3) 2 (the square – (x – 3) has been shifted up five units). ![]() The original function might be: linear, polynomial, square (quadratic), absolute value, square root, rational, sine or cosine. Step 1: Identify the original function(s). Function TypeĮxample problem 1: Identify the functions in the equation f(g(x)) = -(x – 3) 2 + 5 ![]() In order to be able to decompose a function, you must be able to recognize these forms. Those “basic pieces” are going to have one of the following eight forms. The question becomes what function is f(x) and what function is g(x)? Function Composition: Basic Function Typesįunction decomposition is, in a very basic sense, splitting a complicated function into basic pieces. Is a composite function with f(x) taking an action on g(x). Composite functions are usually represented by f(x) and g(x), where f(x) is a function that takes some kind of action on g(x). Splitting a function into two can be useful if the original composite function is too complicated to work with.
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