In the context of functions, what does (f+g)(x) represent?

In the context of functions, (f + g)(x) represents the sum of the outputs of the functions f and g. This expression is defined as follows: for any input value x, (f + g)(x) is calculated by taking the output of the function f for that input and adding it to the output of the function g for the same input. Mathematically, this is expressed as (f + g)(x) = f(x) + g(x).

This definition holds true for any two functions where addition is defined. The resulting function (f + g) is itself a new function, which combines the effects of both original functions by performing addition on their outputs. Understanding this process is crucial as it helps in exploring operations involving multiple functions, allowing for the study of new behaviors and relationships between them.

The other choices relate to different operations: the product pertains to multiplication of outputs, the difference deals with subtracting one function's output from another, and the composite function involves applying one function to the result of another. Each of these involves a different mathematical operation, reinforcing the importance of recognizing the operations indicated by the notation used.