Function Composition Calculator
Easily calculate the composition of functions f(g(x)) online. Enter your outer function f(x) and inner function g(x) to find the composite function. Step-by-step function composer.
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.