Composite Function Range Calculator

Discover the range of composite functions effortlessly. Enter your functions and visualize the results.

Enter Functions

Outer Function f(x):

Enter the outer function in terms of x.

Inner Function g(x):

Enter the inner function in terms of x.

Range of f(g(x)):

Function Visualization

Understanding Composite Functions and Range

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)) means we first apply g to x to get g(x), and then apply f to the result to get f(g(x)). The range of a function is the set of all possible output values. For a composite function f(g(x)), the range is determined by considering the possible outputs of g(x) that are valid inputs for f(x). This tool helps you calculate and visualize the range of such composite functions. Simply input your functions f(x) and g(x) to explore their composite behavior and range.

f(x): The outer function. This function is applied last.
g(x): The inner function. This function is applied first.
Range: The set of all possible output values of f(g(x)).