Lindotaaa

Páginas: 10 (2380 palabras) Publicado: 26 de noviembre de 2009
FUNCIONES
PRÁCTICA Nº 01: OBTENER EL DOMINIO Y RANGO

1. [pic]
(x2 - 9)1/2 R ≥ 0
(x2 - 9) ≥ 0 Rango = R ≥ 0
(x2 - 32) ≥ 0 Dom = [3; +8]
[pic] x – 3 = 0 ( x + 3 = 0
x = 3 x = -3

2. g(x) = Ln [pic]
a > 0
4 - x2 > 0
(x - 2) (x + 2) > 0
X -2 = 0 x + 2 = 0
X = 2 x = - 23. h(x) = [pic]
x2 – 4 = 0
x2 = 4
x = [pic] Dom: [2, ∞>
x = 2 Ran: R ≥ 0

4. K(x) = -3 - [pic]
K(x) = - 3 – (x – 5) ½ Rango: R ≥ 0
(x – 5 ) = 0 Dom: [5, ∞-1>
x = 5

3. Si f(x) = -3 - [pic] y g(x) = 3x2, determina:

|fog = f(3x2) |(g o f) = g(-3 - [pic])|
|= -3 - [pic] |= (3)(-3-[pic])2 |
|= 3x – 3x - [pic] |= 3(9 – x - 5) |
|= 3x - [pic] + 3 |= 37 – 3x – 15|
|= 3x – 5.5 |= 3x – 12 |
|Dom (f o g) = R |Dom (g o f) = R |

4. Dibuja, a mano, una esquema aproximado de la gráfica de cada función
a) y = x3
x =-3 ( y = -27
x = -2 ( y = -8
x = -1 ( y = -1
x = 0 ( y = 0
x = 1 ( y = 1
x = 2 ( y = 8
x = 3 ( y = 9

b) y = senx

c) y = x4
x = -3 ( y = -81
x = -2 ( y = -16
x = -1 ( y = --1
x = 0 ( y = 0
x = 1 ( y = 1
x = 2 ( y = 16
x = 3 ( y = 81

d) y = [pic]
x = 1 ( y = 1
x = 4( y = 2
x = 9 ( y = 3
x = 16 ( y = 4
x = 25 ( y = 5
x = 36 ( y = 6

e) y = cosx

5. Dadas las funciones F(x) = x + 2 y g(x) = [pic] determina cuales de los siguientes enunciados son correctos

|Dfog = Dgof |D (g o f) (x) = g (f(x)) |
|(f o g) (x) = f(g(x))|= g(x + 2) |
|= [pic] |= [pic] |
|= [pic] + 2 |= [pic] |
|= [pic]|x+3≠0 D(gof)=R-{-3} |
|= x+1≠0 |x ≠ -3 |
| |Dfog ≠ Dgof |
|Dom (fog) = R – (1)| |
| |FALSO |

a) (g o f) (x) = g (x + 2)

b) [pic]
[pic]
Reemplazo (-1)
(x + 2) (x + 1)
Verdadero ( (-1 + 2) (-1 +1) = 0

c) [pic]
[pic]
Reemplazo por -2
[pic]