f 2 2 4 j f x x 2 2 g f 2 i g f x x x 3 1 2 2 f g 2 2 h f f g x x x x 2 3 2 1 2

F 2 2 4 j f x x 2 2 g f 2 i g f x x x 3 1 2 2 f g 2 2

This preview shows page 321 - 325 out of 640 pages.

( )( ) f 2 2 4 = j) ( )( ) f x x 2 2 = + g f ( ) 2 i) g f x x x = + ( ) ( ) 3 1 2 2 ( )( ) f g = − 0 2 2 h) ( )( ) f f g x x x x + = + + + 2 3 2 1 2 ( )( ) g f = 3 3 8 5 g) ( )( ) g f x x x = + 3 1 2 2 ( )( ) g f + = + 5 1 8 7 f ) ( )( ) g f x x x + = + + 3 1 2 2 ( )( ) f f = 2 4 e) ( )( ) f f x x = + 2 f g = ( ) 2 0 d) f g x x x = + ( ) ( ) 2 1 2 3 ( )( ) f g = − 0 3 2 c) ( )( ) f g x x x = + 3 2 1 2 ( )( ) f g = 3 5 3 8 b) ( )( ) f g x x x = + 2 3 1 2 ( )( ) f g + = + 5 7 1 8 a) ( )( ) f g x x x + = + + 2 3 1 2 f g ( ) 2 g f ( ) 2 g x x ( ) = 3 1 2 f x x ( ) = + 2 041 Y X 2 2 f ( x ) f ( x ) Y X 2 2 f ( x ) f ( x ) d) = − f x x ( ) 8 c) f x x ( ) = − 8
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322 Calcula el dominio de las funciones. Utiliza el resultado para calcular el dominio de las siguientes funciones. a) ( f + g )( x ) c) b) ( f g )( x ) d) Dom f = ( , 2] [2, + ) Dom g = [ 5, 5] a) Dom ( f + g ) = [ 5, 2] [2, 5] b) Dom ( f · g ) = [ 5, 2] [2, 5] Dadas las funciones: n ( x ) = x + 6 define las siguientes funciones y determina sus dominios. a) ( m + n )( x ) c) b) ( n + p )( x ) d) ( m n + p )( x ) Dom ( m + n ) = ( , 2] [2, + ) Dom ( n + p ) = R { 1} Dom ( m · n + p ) = ( , 2] [2, + ) d) ( )( ) ( ) m n p x x x x x + = + + + 2 4 6 1 1 Dom n m = − + ( , ) ( , ) 2 2 c) n m x x x = + ( ) 6 4 2 b) ( )( ) n p x x x x + = + + + 6 1 1 a) ( )( ) m n x x x + = + + 2 4 6 n m x ( ) p x x x ( ) = + 1 1 m x x ( ) = 2 4 043 d) Dom [ g f = − 5 2 2 5 , ) ( , ] c) Dom f g = − ( , ] [ , ) 5 2 2 5 g f x ( ) f g x ( ) g x x ( ) = 25 2 f x x ( ) = 2 4 042 Funciones
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323 Dadas las funciones: f ( x ) = 2 x g ( x ) = x 2 calcula las composiciones de funciones. a) f g d) g f b) g h e) h g c) h f f ) f h Determina el valor de cada función para x = 3. Comprueba con las funciones y g ( x ) = 3 x 2 que la composición de funciones no es conmutativa. Calcula el dominio de f g y de g f . ( f g )( x ) ( g f )( x ) La composición de funciones no es conmutativa. Dom ( ) [ , ) g f = − + 1 Dom ( ) , f g = + 1 3 ( )( ) ( ( )) g f x g f x g x x = = + ( ) = + 1 3 1 2 ( )( ) ( ( )) ( ) f g x f g x f x x = = = 3 2 3 1 f x x ( ) = + 1 045 ( )( ) f h 3 2 3 = f) ( )( ) ( ( )) f h x f h x f x x = = = 1 2 1 ( )( ) h g 3 1 9 = e) ( )( ) ( ( )) ( ) h g x h g x h x x = = = 2 2 1 ( )( ) g f 3 64 = d) ( )( ) ( ( )) ( ) g f x g f x g x x = = = 2 2 2 ( )( ) h f 3 1 8 = c) ( )( ) ( ( )) ( ) h f x h f x h x x = = = 2 1 2 ( )( ) g h 3 1 9 = b) ( )( ) ( ( )) g h x g h x g x x = = = 1 1 2 ( )( ) f g 3 512 = a) ( )( ) ( ( )) ( ) f g x f g x f x x = = = 2 2 2 h x x ( ) = 1 044 7 SOLUCIONARIO
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324 Explica de qué manera hay que componer las funciones: g ( x ) = 5 x + 1 para obtener las siguientes funciones.
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