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f(x+y)=f(x).f(y)+g(x).g(y)

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Sejam ( ) 
 
 
( ) e ( ) 
 
 
( ). Mostre que ( ) ( ) ( ) ( ) ( ). 
Para ( ) 
 
 
( ) , temos: 
 ( ) 
 
 
( ) 
 ( ) 
 
 
( ) 
Para ( ) 
 
 
( ) , temos: 
 ( ) 
 
 
( ) 
 ( ) 
 
 
( ) 
Para ( ) ( ) ( ) ( ) ( ), temos: 
 ( ) 
 
 
( ( ) ( )) 
 ( ) ( ) ( ) ( ) [
 
 
( )] [
 
 
( )] [
 
 
( )] [
 
 
( )] 
 
 
 
[( ) ( )] 
 
 
[( ) ( )] 
 
 
 
 ( ) 
 
 
 ( ) 
 
 
 
 ( ) 
 
 
 ( ) 
 
 
 
 ( ( )) 
 
 
 ( ( )) 
 
 
 
 
 
 
 
 
 
 
 
 
 ( ) 
 
 
 
 
 
 
 
 
 
 
 
 ( ) 
 
 
 
 
 
 
 
 
 
 
 
 
 ( ) 
 
 
 
 
 
 
 
 
 
 
 
 ( ) 
 
 
 
 
 
 
 ( ) 
 
 
 
 
 
 ( ) 
 
 
 
 
 
 ( ) 
 
 
 
 
 
 ( ) 
 
 
 
 ( ( )) 
Então ( ) ( ) ( ) ( ) ( ).

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