sea f(x): x3 -3, g(x): 2x + 8 y h(x): 4x3 + 3.
Determina
(f + g) 3
g +h
f - g
(g-h)(1/4)
(f/h)(3) - g(-1)
Respuestas
Los valores de las operaciones de funciones son :
(f + g) 3 = 38
( g +h)(x) = 4x3 + 2x + 11
( f - g)(x) = x3 -2x+ 5
(g-h)(1/4) = 87/16
(f/h)(3) - g(-1) = -214/37
Para calcular los valores de las operaciones de las funciones se procede de la siguiente manera :
f(x)= x3 -3
g(x) =2x + 8
h(x)= 4x3 + 3
(f + g) 3
= ( x3 -3 ) + ( 2x + 8 ) = x3 +2x+5
= ( 3)³ + 2*3 + 5 = 27 + 6+5 = 38 .
( g +h )(x) = ( 2x+8 ) + ( 4x3 +3 ) = 4x3 + 2x + 11 .
( f - g )(x) = ( x3 -3 ) - ( 2x + 8 ) = x3 -2x+ 5
(g-h)(1/4) = ( 2x +8 ) - ( 4x3 +3) = - 4x3 + 2x + 5
= -4* ( 1/4)³+ 2* ( 1/4)+ 5 = 87/16
( f/h ) (x) = ( x3-3)/(4x3 +3 )
( f/h ) (3) = ( 3³-3)/(4*3³ +3 ) = 24/111
g(-1) = 2* ( -1) + 8 = -2+8 = 6
(f/h)(3) - g(-1) = 24/111- 6 = -214/37