# 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
*
).