b n x 25 x 6 Determina f f 1 y f 1 f en los pares de funciones para comprobar

B n x 25 x 6 determina f f 1 y f 1 f en los pares de

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b) n ( x ) = 25 x + 6 Determina f f 1 y f 1 f en los pares de funciones para comprobar si son inversas o no. a) f ( x ) = 3 x 1 y b) f ( x ) = 2 x y c) f ( x ) = 2 x y f 1 ( x ) = log 2 x d) f ( x ) = sen x y f 1 ( x ) = arc sen x e) f ( x ) = x 2 + 2 y Las funciones no son inversas. Las funciones no son inversas. Las funciones son inversas. Las funciones son inversas. Las funciones son inversas. e) ( )( ) ( ( )) ( f f x f f x f x x x f f = = ( ) = + = 1 1 1 2 2 2 )( ) ( ( )) ( ) x f f x f x x x = = + = + = 1 1 2 2 2 2 2 d) ( )( ) ( ( )) ( ) ( f f x f f x f arc sen x sen arc se = = = 1 1 n x x f f x f f x f sen x arc sen ) ( )( ) ( ( )) ( ) = = = = 1 1 1 ( ) sen x x = c) ( )( ) ( ( )) (log ) ( log f f x f f x f x x f x = = = = 1 1 2 2 2 1 1 1 2 2 2 f x f f x f x x x )( ) ( ( )) ( ) log = = = = b) ( )( ) ( ( )) f f x f f x f x = = 1 1 1 2 = = 2 1 2 1 1 x f f x f ( )( ) ( f x f x x ( )) ( ) = = 1 2 2 1 2 a) ( )( ) ( ( )) f f x f f x f x = = + = 1 1 1 3 1 3 1 3 1 1 2 1 1 x x f f x f f x + = + = = ( )( ) ( ( )) f x x x ( ) = + = + 1 3 1 1 3 3 1 1 2 3 ( ) f x x = 1 2 ( ) f x x = 1 1 2 ( ) f x x = + 1 1 3 1 ( ) 047 c) ( )( ) ( ( )) g h x g h x g x x = = + = + + 2 1 10 1 1 = + + = x x p x 11 1 ( ) b) ( )( ) ( ( )) ( ) ( ) g g x g g x g x x x = = + = + + = + = 5 1 5 5 1 1 25 6 n x ( ) a) ( )( ) ( ( )) ( ) g f x g f x g x x m x = = + ( ) = + + = 2 2 4 5 4 1 c) p x x x ( ) = + + 11 1 a) m x x ( ) = + + 5 4 1 2 h x x ( ) = + 2 1 f x x ( ) = + 2 4 046 Funciones
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325 Calcula la función inversa de cada función. a) y = 2 x + 5 b) c) Comprueba que sus gráficas son simétricas respecto a la bisectriz del primer cuadrante. Y X 1 f ( x ) f 1 ( x ) 1 c) y x x y f x x = = + = + 2 3 3 2 3 2 3 3 1 3 ( ) Y X 2 f ( x ) f 1 ( x ) 2 b) y x x y f x x = = = 3 2 3 2 3 2 1 ( ) Y X 2 2 f ( x ) f 1 ( x ) a) y x x y f x x = + = = 2 5 5 2 5 2 1 ( ) y x = 2 3 3 y x = 3 2 048 7 SOLUCIONARIO
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326 Dada la gráfica de la función y = x 3 : dibuja la gráfica de su función inversa. Dibuja las funciones inversas. a) b) 1 1 X Y y = 1 + 2 x 1 1 X Y y = ln ( x + 3) 050 1 1 X Y f ( x ) f 1 ( x ) 1 1 X Y y = x 3 049 Funciones
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327 c) d) Y X 1 1 f ( x ) f 1 ( x ) d) Y X 1 1 f ( x ) f 1 ( x ) c) Y X 1 1 f ( x ) f 1 ( x ) b) Y X 2 2 f ( x ) f 1 ( x ) a) 1 1 X Y y = 2 x 1 1 1 X Y y x = + 1 2 log 2 7 SOLUCIONARIO
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328 Dibuja funciones que cumplan estas propiedades. a) Su dominio y su recorrido son R . b) Su dominio es R {1}. c) Es creciente y su dominio es R { 1, 2}. d) Es logarítmica y su dominio es (3, + ). e) Es logarítmica y su dominio es ( , 2). f) Es exponencial y su dominio es R {0}. Respuesta abierta. En una vivienda pagan 10 euros de gasto fijo y 0,50 euros por cada kilovatio consumido a la empresa que les suministra electricidad. a) Obtén una expresión de la relación que existe entre el consumo y el precio y represéntala.
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