{x x∈ Df ∩ D - Acerca del Departamentodepar ?· ... = +2 1 2 gx x( ) = +8 4 iv) f x( ) x = + 1 1…

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55INTRODUCCIN A LA MATEMTICA SUPERIOR OPERACIONES CON FUNCIONES Suma, diferencia, producto y cociente de funciones Terminologa Valor de la funcin Dominio Suma gf + ( )( ) ( ) ( )xgxfxgf +=+ gfgf DDD =+ Diferencia gf ( )( ) ( ) ( )xgxfxgf = gfgf DDD = Producto fg ( )( ) ( ) ( )xgxfxfg = gffg DDD = Cociente gf ( )( )( )xgxfxgf={ }0)(,/ = xgDDxxD gfgf OBSERVACIN: SIEMPRE ( )( ) ( ) ( )xgxfxgf +=+ PERO NO SIEMPRE ( ) ( ) ( )bfafbaf +=+ POR EJEMPLO: Sea ( ) xxf = entonces si 0ab , ( ) ( ) ( )bfafbaf ++ OF1.- Con la informacin que aparece en las tablas determinar el dominio y la funcin resultante de la operacin que se indica en cada inciso. x 0 2 4 6 7 10 x 0 2 3 6 7 f(x) 2 15 3 8 2 1 g(x) 1 3 5 2 0 a) gf + b) fg c) gf OF2.- Si las funciones f y g estn definidas por ( ) ( ) ( ){ }4,3,3,2,2,1:f y ( ) ( ) ( ){ }8,4,5,3,3,1:g determinar el dominio y la funcin resultante de la operacin que se indica en cada inciso. a) gf + b) fg c) gf OF3.- Si ( )f x x= 3 , ( )g xx=18 calcular: a) ( ) ( )44 gf b) ( )( )2fg OF4.- ( )f xx=+11 ( )g x = 5 calcular: a) ( ) ( )11 gf b) ( )( )2fg 56OF5.- Si ( )f x x x= + 2 y ( )g xxxsisixx=< 4522 encontrar los siguientes valores: a) ( ) ( )f g 5 3 b) ( )( )2fg c) ( )( )4gf + OF6.- Calcular en cada caso a) ( ) ( )f x g x+ , b) ( ) ( )f x g x , c) indicar dominio y rango. i) ( )f x x= +2 3, ( )g x x= +5 4 ii) ( )f x x= +121, ( )g x x= 2 32 iii) ( )f x x= +3 22 , ( )g x x= 1212 iv) ( )f xx=+11, ( )g x = 5 v) ( )f x x= 2 3 , ( )g x = 4 vi) ( )f x x= 3 , ( )g xx=18 vi) ( )f x x= + 8 , ( )g x x= 17 OF7.- Calcular en cada caso a) ( ) ( )f x g x , b) ( )( )f xg x, c) indicar el dominio de ( )f x , ( )g x , ( )( )f xg x y ( ) ( )f x g x . i) ( )f x x= +5 2 , ( )g x x= 3 1 ii) ( )f x x= 3 12 , ( )g x x= +134 iii) ( )f x x= +2 12 ( )g x x= +8 42 iv) ( )f xx=+11, ( )g x x= +2 2 v) ( )f x x= 5 53 , ( )g x x= +5 5 vi) ( )f x x= 3 , ( )g x x=18 OF8.- Calcular 18.- ( )f xx si xx si xx si x=

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