Function Composition Calculator
Discover how functions interact! Enter the outer function f(x) and the inner function g(x) to compute their composition f(g(x)).
Enter Your Functions
Define the outer function f(x) and the inner function g(x). Use standard mathematical notation (e.g., x^2, sin(x), 2*x+3).
Enter the function that will be evaluated first.
Enter the function that will be substituted into f(x).
Result: Composition f(g(x))
The composition of f(x) and g(x), denoted as f(g(x)), is:
Calculation Steps:
Understanding Function Composition
In mathematics, function composition is a way to combine two functions such that the output of one function becomes the input of another function. Specifically, the composition of a function f with a function g is denoted as f(g(x)). This means that you first apply the function g to x to get g(x), and then apply the function f to the result, g(x), to get f(g(x)).
For example, if f(x) = x² and g(x) = x + 1, then f(g(x)) = f(x + 1) = (x + 1)². This calculator helps you compute the composite function f(g(x)) for any given functions f(x) and g(x).
- Outer Function (f(x)): The function that is applied second. It's the 'outer' layer in the composition.
- Inner Function (g(x)): The function that is applied first. Its result is 'input' to the outer function.
- Composite Function (f(g(x))): The resulting function after applying function composition.
Learn more about function composition on resources like Wikipedia or Khan Academy.