Composite Function Domain Calculator
Easily calculate the domain of a composite function f(g(x)) online. Input the outer function f(x) and inner function g(x) to find the domain. Free and user-friendly tool.
Enter Functions
Input the outer function f(x) and the inner function g(x).
Domain of f(g(x)):
Domain Visualization
The domain of f(g(x)) is , which means the composite function is defined for all real numbers. This is visualized on the number line below.
Understanding Composite Function Domain
In mathematics, a composite function is a function that is formed by combining two functions. If we have two functions, f(x) and g(x), the composite function f(g(x)) is obtained by substituting g(x) into f(x).
The domain of a composite function f(g(x)) is the set of all x values such that x is in the domain of g and g(x) is in the domain of f. In simpler terms, you first apply g to x, and then apply f to the result g(x). For f(g(x)) to be defined, both operations must be valid.
For example, if f(x) = √x and g(x) = x - 1, then f(g(x)) = √(x - 1). The domain of g(x) is all real numbers, but the domain of f(x) is x ≥ 0. Therefore, for f(g(x)) to be defined, we need g(x) ≥ 0, which means x - 1 ≥ 0, or x ≥ 1. So, the domain of f(g(x)) is [1, ∞).
For more information, you can refer to resources like: Wikipedia - Composite Function