# Composite function

Consider the function:

*y =*sin

^{ 2 }( 2

*x*) .

Actually, this record means the following chain of functional transformations:

*u*= 2

*x*-->

*v*= sin

*u*-->

*y = v*

^{ 2 }

*,*

that can be written by symbols of functional dependences in a general view as:

*u*=

*f*

_{ 1 }

*(*

*x*) -->

*v*=

*f*

_{ 2 }(

*u*) -->

*y = f*

_{ 3 }

*(*

*v*) ,

or more shortly:

*y = f*{

*v*[

*u*(

*x*) ] }.

We have here not the one rule of correspondence to transform
*
x
*
into
*
y
*
, but
three consecutive rules (functions), using which we receive
*
y
*
from
*
x
*
. In this case we say that
*
y
*
is a
*
composite function
*
of
*
x
*
.

E x a m p l e . The following functions are composite ones:

Write, please, the two rest functions like this.