The document provides exercises on composition of functions. It gives the definitions of various functions f(x) and g(x) and asks to calculate f(x)+g(x), f(x)-g(x), f(x)*g(x), fog(x), gof(x), fof(x), and gog(x) for different functions f(x) and g(x). It provides 30 problems to calculate the composition of the given functions through addition, subtraction, multiplication and composition of functions.

1. Universidad Técnica del Norte
Composición de funciones
Ejercicios
PAOLA SARAUZ
13

2. * Resolver los siguientes ejercicios hallando las cuatro operaciones fundamentales.
16.- Si f(x)=x+2
a) f(x)+g(x)= x+2+ x2-2x+1
f(x)+g(x)= x2-x+3
g(x)=x2-2x+1
b) f(x)-g(x)= x+2- x2+2x-1
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
a) f(x)+g(x)= 3x2-2x+1+ x-4
f(x)+g(x)= 3x2-x-3
g(x)=x-4
b) f(x)-g(x)= 3x2-2x+1- x-4
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
x
a) f(x)+g(x)=
g(x)=x-3
b) f(x)-g(x)=
f(x)+g(x)=
f(x)-g(x)=
f(x)+g(x)=
c) f(x)*g(x)=
x
f(x)+g(x)=x
x
(x-3)
d)
f(x)*g(x)=
x
f(x)*g(x)=
19.- Si f(x)=2x-1
a) f(x)+g(x)= 2x-1+ x2+1
f(x)+g(x)= x2+2x
c) f(x)*g(x)= (2x-1)(x2+1)
g(x)= x2+1
b) f(x)-g(x)= 2x-1-x2-1
f(x)-g(x)= x2-2x+2
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

3. x
a) f(x)+g(x)=
b) f(x)-g(x)=
f(x)+g(x)=
f(x)-g(x)=
f(x)+g(x)=
c) f(x)*g(x)= x
x
f(x)+g(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
2+5x+2
f(x)+g(x)= 2x
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
a) f(x)+g(x)= x3+1+ x+1
f(x)+g(x)= x3+x+2
c) f(x)*g(x)=( x3+1)(x+1)
g(x)=x+1
b) f(x)-g(x)= x3+1- x-1
f(x)-g(x)= x3- x
d)
f(x)*g(x)= -x4+x3x+1
x
23.- Si f(x)=x2+7
a) f(x)+g(x)= x2+7+5x+3
f(x)+g(x)= x2+5x+10
x
g(x)=5x+3
b) f(x)-g(x)= x2+7-5x-3
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
a) f(x)+g(x)= x3 +9x+5
c) f(x)*g(x)= (x3)(9x+5)
f(x)*g(x)= 9x4+5x3
g(x)=9x+5
d)
b) f(x)-g(x)= x3-9x-5

4. 25.- Si f(x)=x2+3
a) f(x)+g(x)= x2+3+2x+57
f(x)+g(x)=x2+2x+60
g(x)=2x+57
b) f(x)-g(x)= x2+3-2x-57
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
2-2x+1+2= x2-2x+3
a) (fog)(x)=x
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
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
g(x)=x+1
28.- Si f(x)=x+2
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
g(x)=x-1
29.- Si
f(x)=
g(x)=
a) (fog)(x)= ( x
)
(
)
x
x
b) (gof)(x)= ( x
)
(
)
x
x
c) (fof)(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
x