# 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

v

=

*f*

_{2}(

*u*)

–>

y = f

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.