Definition of function: Generally speaking, there are two variables X and Y in a changing process. If a value of X is given and a unique Y is determined accordingly, Y is said to be a function of X, where X is an independent variable and Y is a dependent variable. The range of x is called the domain of the function, and the range of y is called the domain of the function.
F is a bridge between independent variables and dependent variables. For example, Y = x 2-2x+3. How do x and y correspond here (meaning f)? That is, subtract the square of the independent variable (x) twice and add 3 to get the dependent variable.
As for what you said about 2f, 3f and 4f, I don't know what it means. You can think that f(x) is a genetic variable. 2f (x) and 3f (x) represent double f(x) and triple f(x).
The square of f(x) can be written as follows: f 2 (x), that is, write a "2" in the upper right corner of f.