Composite Function Decomposition Calculator
Easily decompose a composite function h(x) into its outer function f(x) and inner function g(x). Understand function composition with this interactive tool.
Enter the composite function you want to decompose.
Decomposition Result:
This tool decomposes h(x) into f(x) and g(x) such that h(x) = f(g(x)). It identifies potential outer and inner functions based on the structure of the input composite function.
Understanding Composite Function Decomposition
In mathematics, especially in calculus, decomposing a composite function is the process of expressing a function as a composition of two or more simpler functions. Given a composite function h(x), we aim to find functions f(x) and g(x) such that h(x) = f(g(x)). Here, g(x) is often referred to as the inner function, and f(x) as the outer function.
For example, if h(x) = sin(2x), we can decompose it into f(x) = sin(x) and g(x) = 2x, because f(g(x)) = f(2x) = sin(2x) = h(x). This tool helps you find such decompositions for various composite functions. Note that for some functions, decomposition might not be unique or even possible in simple terms.
Learn more about function composition on Wikipedia.