Designation of functions
Let y be some function of variable x ; moreover, it is not essential, how this function is given: by formula or by table or by any other way. Only the fact of existence of this functional dependence is important. This fact is written as: y = f ( x ). The letter f ( it is initial letter of Latin word “functio” – a function ) doesn’t mean any value, as well as letters log , sin , tan in the functions y = log x , y = sin x , y = tan x. They say only about the certain functional dependence y of x . The record y = f ( x ) represents any functional dependence. If two functional dependencies y of x and z of t differ one from the other, then they are written using different letters, for instance: y = f ( x ) and z = F ( t ). If some dependencies are the same, then they are written by the same letter f : y = f ( x ) and z = f ( t ). If an expression for functional dependence y = f ( x ) is known, then it can be written using both of the designations of function. For instance, y = sin x or f ( x ) = sin x . Both shapes are equivalent completely. Sometimes another form of functional dependence is used: y ( x ). This means the same as y = f ( x ).