Universidad Técnica del Norte

13

Composición de funciones Ejercicios

PAOLA SARAUZ

* Resolver los siguientes ejercicios hallando las cuatro operaciones fundamentales. 16.- Si f(x)=x+2 g(x)=x2-2x+1 a) f(x)+g(x)= x+2+ x2-2x+1 b) f(x)-g(x)= x+2- x2+2x-1 f(x)+g(x)= x2-x+3 f(x)-g(x)= x2-3x-1

c) f(x)*g(x)= (x+2)(x2-2x+1) d)

f(x)*g(x)= x3-2x2+x+2x2-4x+2 f(x)*g(x)= x3-3x+2 17.- Si f(x)=3x2-2x+1 g(x)=x-4 a) f(x)+g(x)= 3x2-2x+1+ x-4 b) f(x)-g(x)= 3x2-2x+1- x-4 f(x)+g(x)= 3x2-x-3 f(x)-g(x)= 3x2-3x+5

c) f(x)*g(x)= (3x2-2x+1)( x-4) d)

f(x)*g(x)= 3x3-12x2+x-2x2+8x-4 f(x)*g(x)= 3x3-4 x2+9x-4

18.- Si f(x)=

si x≠0 g(x)=x-3

a) f(x)+g(x)=

x b) f(x)-g(x)=

x

f(x)+g(x)=

f(x)-g(x)=

f(x)+g(x)=

f(x)+g(x)=-

c) f(x)*g(x)= x

x (x-3) d)

f(x)*g(x)=

x

f(x)*g(x)=

19.- Si f(x)=2x-1 g(x)= x2+1 a) f(x)+g(x)= 2x-1+ x2+1 b) f(x)-g(x)= 2x-1-x2-1 f(x)+g(x)= x2+2x f(x)-g(x)= x2-2x+2

c) f(x)*g(x)= (2x-1)(x2+1) d)

f(x)*g(x)= 2x3+2x-x2-1 f(x)*g(x)= 2x3-x2+2x-1

20.- Si f(x)=

g(x)= x2-1

a) f(x)+g(x)=

x b) f(x)-g(x)=

x

f(x)+g(x)=

f(x)-g(x)=

f(x)+g(x)=

f(x)+g(x)=-

c) f(x)*g(x)= x

x (x-1)(x+1) d)

f(x)*g(x)=x2+x

x x

21.- Si f(x)=-x2+3x+1 g(x)=3x2+2x+1 a) f(x)+g(x)= -x2+3x+1+3x2+2x+1 b) f(x)-g(x)= -x2+3x+1-3x2-2x-1 f(x)+g(x)= 2x2+5x+2 f(x)-g(x)= -4x2+x

c) f(x)*g(x)= (-x2+3x+1)+3x2+2x+1) d)

f(x)*g(x)= -2x4-5x3-2x2+6 x3 +15x2+6x+2x2+5x+2 f(x)*g(x)= -2x4+x3+15x2+11x+2 22.- Si f(x)= x3+1 g(x)=x+1 a) f(x)+g(x)= x3+1+ x+1 b) f(x)-g(x)= x3+1- x-1 f(x)+g(x)= x3+x+2 f(x)-g(x)= x3- x

c) f(x)*g(x)=( x3+1)(x+1) d)

f(x)*g(x)= -x4+x3x+1

x x

23.- Si f(x)=x2+7 g(x)=5x+3 a) f(x)+g(x)= x2+7+5x+3 b) f(x)-g(x)= x2+7-5x-3 f(x)+g(x)= x2+5x+10 f(x)-g(x)= x2-5x+4

c) f(x)*g(x)= (x2+1)(5x+3) d)

f(x)*g(x)= 5x3+3x2+35x+21 24.- Si f(x)=x3 g(x)=9x+5 a) f(x)+g(x)= x3 +9x+5 b) f(x)-g(x)= x3-9x-5

c) f(x)*g(x)= (x3)(9x+5) d)

f(x)*g(x)= 9x4+5x3

25.- Si f(x)=x2+3 g(x)=2x+57 a) f(x)+g(x)= x2+3+2x+57 b) f(x)-g(x)= x2+3-2x-57 f(x)+g(x)=x2+2x+60 f(x)-g(x)= x2-2x-54

c) f(x)*g(x)= (x2+3)(2x+57) d)

f(x)*g(x)= 2x3+57x2+6x+171 * Resolver los siguientes problemas de composición de funciones hallando en todos: (fog)(x), (gof)(x), (fof)(x), (gog)(x). 26.- Si f(x)=x+2 g(x)=x2-2x+1 a) (fog)(x)=x2-2x+1+2= x2-2x+3 b) (gof)(x)=(x+2)2-2(x+2)+1=x2+4x+4-2x-4+1=x2+2x+1 c) (fof)(x)=x+2+2=x+4 d) (gog)(x)=(x2-2x+1)-2x2+4x-2+1=8x6+3x4+10x2+4x 27.- Si f(x)=5x/3 g(x)=x+1 a) (fog)(x)=5(x+1)/3=5x+5/3 b) (gof)(x)=5x/3 +1=5x+3/3 c) (fof)(x)=5(5x/3)/3=25x/9 d) (gog)(x)=x+1+1=x+2 28.- Si f(x)=x+2 g(x)=x-1 a) (fog)(x)=x-1+2=x+1 b) (gof)(x)=x+2-1=x+1 c) (fof)(x)=x+2+2=x+4 d) (gog)(x)=x-1-1=x-2

29.- Si f(x)=

g(x)=

a) (fog)(x)= ( x

)

(

)

x

x

b) (gof)(x)= ( x

)

(

)

x

x

c) (fof)(x)= ( x

)

(

)

x

d) (gog)(x)= ( x

)

(

)

x

30.- Si f(x)=5x+1 g(x)=3-9x a) (fog)(x)=5(3-9x)+1=15-45x+1=16-45x b) (gof)(x)=3-9(5x+1)=3-45x-9=12-45x c) (fof)(x)=5(5x+1)+1=25x+5+1=25x+6 d) (gog)(x)=3-9(3-9x)=3-27+81x=81x-24