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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 xy = sin xy = 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 ).

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