If given two functions f(x) and g(x), how is their sum represented?

The sum of two functions, f(x) and g(x), is mathematically defined by combining their outputs. This is represented by the notation (f + g)(x), which signifies that for a given input x, you take the value of f at that input and add it to the value of g at that same input. Therefore, (f + g)(x) = f(x) + g(x) accurately describes this operation.

This way of defining the sum of functions is a fundamental aspect of understanding how functions interact with each other. When you see the notation (f + g)(x), it is clear that you are performing addition on the outputs of f and g. This concept is pivotal in calculus, algebra, and many other branches of mathematics, as it establishes a basis for further operations involving functions, such as composition and transformation.

In contrast, the other representations either describe different operations or are incorrect in their notation. The correct representation ensures clarity in mathematical communication regarding how the functions relate to each other when added.