What is the representation of a composite function?

In mathematics, a composite function is formed by combining two functions in such a way that the output of one function becomes the input of another. When we denote this operation with two functions f and g, the composite function is written as f(g(x)), which means we take the function g, apply it to x, and then take the result and apply the function f to that result.

This structure relies on the order of operations: you first evaluate g at x, and then pass that output to f. The expression f(g(x)) clearly captures this sequential action and underscores how the two functions interact with each other through their inputs and outputs.

In contrast, the other choices do not represent the concept of a composite function. The notation f * g(x) suggests multiplication of the function f and the output of g at x, while f/g(x) implies division. Both of these symbols indicate arithmetic operations rather than the relationship involved in composition. Finally, the representation g(f(x)) signifies the opposite composition, where f is applied first, followed by g, and does not reflect the original intent of forming the composite function as described. Thus, f(g(x)) is the correct representation of a composite function, embodying the essence of how functions can be