Function Composition Formula:
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Definition: Function composition combines two functions where the output of one function (g) becomes the input of another (h).
Purpose: It allows creating complex functions by combining simpler ones, which is fundamental in mathematics and computer science.
The composition is represented by:
Where:
Explanation: The output of g(x) is used as the input to h(x), creating a new function that combines both operations.
Details: Composition is used in calculus, functional programming, and mathematical modeling to build complex operations from simple components.
Tips: Enter the algebraic expressions for g(x) and h(x), and optionally a specific x value to evaluate the composition at that point.
Q1: What's the difference between h(g(x)) and g(h(x))?
A: The order matters! h(g(x)) applies g first, then h, while g(h(x)) does the reverse.
Q2: Can I compose more than two functions?
A: Yes, like f(g(h(x))). The calculator can be extended for more functions.
Q3: What functions can I use?
A: Basic operations (+, -, *, /) and common functions (sin, cos, exp, log, etc.) when implemented.
Q4: Does composition always work?
A: The range of g must be compatible with the domain of h for the composition to be valid.
Q5: How is this used in real applications?
A: In physics for combined transformations, in programming for function pipelines, and in math for complex derivations.