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
