What is a composite function?

• A. A function that cannot be decomposed
• B. A function formed by adding two functions together
• C. A function formed when one function is applied to the result of another function
• D. A function with no variables

Answer: (C)

A composite function is created when one function is applied to the output of another function. This process involves taking the result produced by an initial function and using that result as the input for a second function.

Mathematically, if you have two functions, say ( f(x) ) and ( g(x) ), the composite function ( (f \circ g)(x) ) is defined as ( f(g(x)) ). This means you first apply the function ( g ) to ( x ), and then you take that output and apply the function ( f ) to it.

This concept highlights the relationship and order of operations between functions, emphasizing that the output of one function can serve as the input for another, ultimately creating a new function that combines the actions of both.

To clarify the context, a function that cannot be decomposed doesn’t fully encompass the idea of a composite function, and combining functions through addition does not align with the concept of composition, as addition is distinct from the process of applying one function to the result of another. Additionally, a function with no variables does not reflect the nature of composite functions, which typically involve variables as part of their input-output relationships.