Matematicas

1. En los ejercicios 1 a 4 determinar si el conjunto es una función.
Si es una función determine su domino.
2.2 a x,y| y= x+1
b x,y| y= x2-1
c x,y| y= 1-x2
d x,y| x2+y2

Fx= x+1
x+1≥0
X≥-1
Fx= x2-1
x+1x-1≥0
x+1≥0 x-1≥0
x=-1 x=1
Fx= 1-x2
1+x1-x≥0
1+x≥0 1-x≥0
x=-1 x=1
Fx= x2+y2=1
No es función

2.3 ax,y| y= x-12+2
b x,y| x= y-22+1
c x,y| y= x+23-1
d x,y| x= y+13-2

a x,y| y= x-12+2
(x-1)2+2
x2-2x+1+2
x2-2x+3
x2-2x=-3
x(x-2x)=-3
x-1x-1
x=+1 x=-1
x=-1
Dom f=R

b x,y| x= y-22+1
(y-2)2+1
y2-4y+4+1
(y2-4y+5)
y-5(y+1)

Rec f= R
v=-b2a f=(-b2a)
v=(0,-2)

c x,y| y= x+23-1
(x+2)3-1
x+3=(x)3+2(x)2+(4)(x)+8x3+2x2+4x+8-1
x3+6x2+4x+7

d x,y| x= y+13-2
(y+1)3-2
y3+3y2+3y2+1-2
y3+3y2+3y2-1
y3+6y2-1

2.4 Dada fx=3x, calcule :
a f1
b f-3
c f6
d f13
e f3a

f f3x
g f(3)f(x)
h fx-3
i fx- f3
j fx+h- f(x)h , h≠0.






(a) F(1) = 3x =31
= 3
(b) F(-3)= 3
=3
(c) F(6)= 3+(6)
=18
(d) F(13)=(13)+(3x)
=3
(e) F(3x)=(3x)+(3x)
=1
(f) (3a)= (3a)+ (3x)
=3
(g) f(3)f(x)=f(3)f(x)+(3x)
=1
(h) F(x-3)= 3x-3=2
=x
(i) F(x) –f(3)=f(3x)-(9x)
= 6

j fx+h- f(x)h, h≠0
=4x+h2- 5x+h+7-(4x2-5x+7)h
=42+8hx+4h2-5x+7-4x2+5x-7h
=8hx2-5h+4h2h
=8x-4+4h

2.5 Dada gx=3x2-4, calcule :
a g-4
b g12
c gx2
d g3x2-4
egx-h
f gx-gh
g gx+h- g(x)h , h≠0.

a) G(-4);
g-4=3(-4)2-4
=3(16)-4
=48-4
=44
b) B) g(12);
g12=3(12)2-4
=3(14)-4
=34-4
=-134
c) C) g(x2);
gx2=3(x2)2-4
=3(x4)-4
=3x4-4
d) g(3x2-4);
g) 3x2-4=3(3x2-4)2-4
=3(9x4-16)-4
=27x4-48-4
=27x4-52

e) gx-h;
g(x-h)=3(x-h)2-4
=3(x2-h2)-4
=3x2-3h2-

f) gx-g(h);
gx-g(h)=(3x2-4)-(3h2-4)
=3x2-4-3h2+4=3x2-3h2
g) gx+h-gxh,h≠0
gx+h-gxh=3(x+h)2-4-(3x2-4)h
=(9x2+2xh+h2)-4-(3x2-4)h
=9x2+2xh+h2-4-3x2+4h
=6x2+2xh+h2h
=6x2+2x+h



1.6 Dada Gx=4-x, calcule :
a G4-x
b G4-x2
c G4-x4
d G4x-x2
e G-x4-4x2
f Gx+h- G(x)h , h≠0



*G4-X=4-(4-X)=4-4+x=x

*G(4-x2)
G(4-x2)=4-(4-x2) =4-4+x2=x2=x

* G(4-x4)
G4-x4=4-(4-x2)=4-4+x4)=x4=x2

*G(4-x2)G(4x-x2)=4-4x-x2=4-4x+x2=x2-4x+4=x-22= (x-2)

*G(-x4-4x2)
-x2-4x2=4-(-x4-4x2)=4+x4+4x2=x4+4x2+4=x2+22
(x2+2)

* gx+h-g(x)h h= 0
gx+h-g(x)h=4-(x+h)-4-xh=4-x+h-4-xh=h-x+4-4-xh

Dom=todos los números reales
contradominio=
a) x
b) x
c) x2
d) (x-2)
e) x2+2
f) H= 0
g) h-x+4-4-xh

2. En los ejercicios 11 a 46, dibuje a mano la grafica de la función y determine su dominoy su contra dominio.

2.1 gx=4-x

Dom g(x)= 
Rec g (x)= 

3.6 Gx=x2+2

a=1 b=0 c=+2
Coord [x]:-b2a = :02(1) =0

Coord[y]: G (-b2a) =g(0)= (0)2 +2 =+2

V= [+2, +∞)
Dominio= todos los números reales
Recorrido=[-2 , +∞)

3.7 fx=(x-1)2

fx= x-12
=x-1x+1
Dom= R
Rec= R

3.8 Fx=9-x
9-x ≥ 0
X≥9
Domf[3,+x)

2.5 gx=4-x2
2+x≥0(2-x)≥0
x≥-2 2≥=2

X+2 | - | + | + |
X-2 | - | - | + |
P.f. | + | - | + |

3.9 fx=x2-1

x2-1≥0
x+1x-1=0
x+1=0 x-1=0
x=-1 x=1
(x+1) | - | + | + |
(x-1) | - | - | + |
P.f | + | - | + |

Dominio
Dom fx= -∞,-1 U [ 1,+∞)
Recorrido
Rec fx=ℝ
Rec fx=(0,+∞)

3.10 Hx=5-x

Dominio =]-∞ +∞ [ =r
Contradominio = [0+∞] =r

3.11 Gx=x2-4x-2

X-2≠0
X≠2
X=Dom G=R-{ 2 }

2.9 fx=2x2+7x+3x+3

=2x+1x+3(x+3)
=2x+1

Dominio
Dom fx= R- -3
Recorrido
REC=(1,α)

2.10 gx=x2-4(x-3)x2-x-6
gx=x2-4x-3x2-x-6

g(x)=x+2x-2(x-3)x-3(x+2)

gx=x-2

Domf=R\{3,-2}
Recf=(-2,+∞)

Tabla de valores |
x | 0 | 2 |
y | -2 | 0 |

2.11 gx=-4 si x ≤3-1 si -2...