What is the appropriate notation for multiplying functions?

The appropriate notation for multiplying functions is represented as (fg)(x). This notation signifies that you are taking two functions, f and g, and multiplying their outputs together for a given input x.

To clarify, when you see (fg)(x), it indicates the operation of multiplying the outputs of the functions f and g at the input x. Specifically, this can be expressed mathematically as f(x) * g(x). The multiplication is performed on the values of the two functions evaluated at the same point, which is a standard way to represent the product of two functions.

In contrast, the other notations represent different operations. For example, (f-g)(x) denotes the subtraction of function g's output from function f's output, and (f+g)(x) signifies the addition of the outputs of functions f and g. The notation (f*x)(x) is not standard for function multiplication and could lead to confusion, as it suggests multiplying the function f with some variable x rather than indicating multiplication between the two functions f and g. Hence, (fg)(x) is the correct choice for indicating the multiplication of two functions.