F(x) means that x is an independent variable and f is a mapping relationship. If y=f(x), then y is a function of x.

F(x+2) also means this.

As for the composite function, f(x+2) is a composite function, and f(g(x)) looks like a composite function. One function is related to x, and the other function takes the range of the previous function as the independent variable.

Domain refers to the value range of independent variables, depending on which numbers f(x) can take, and domain is these numbers.