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Composite function


Consider the function:

y = sin 2 ( 2x ) .

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

u = 2x  -->  v = sin -->  y = v 2 ,

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

u = f1 ( x -->  v = f2  ( u -->  y = f3  ( 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.

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