Matematicas

Álgebra de Funciones


Las funciones se pueden sumar, restar, multiplicar y dividir:

SUMA: fg=f1 +f2 ( Df g = Df ( Df2
RESTA: fr=f1 – f2 ( Df1 ( Df2
MULTIPLICAR: fm=f1*f2 (Dfm=Df1 (Df2
DIVISION fd=f1/f2 (Dfd=Df1(Df2 {aquellos valores que anulen
al denominador}


F1(x) = 2x +5
F2(x) =-2x – 5


|X|F1(x) |F2(x) |Fg(x) |Fr(x) |Fp(x) |Fc(x) |
|0 |5 |-5 |0 |10 |-25 |-1 |
|1 |7 |-7|0 |14 |-49 |-1 |
|-1 |3 |--3 |0 |6 |-9 |-1 |
|2 |9 |-9 |0 |18|-81 |-1 |



Fg (x)=2x + 5 + (-2x –5)
Fg(x) = 0 y =0

Fg(x) = 2x +5 – (-2x –5)
Fg (x) = 4x +10

Fp(x)=(2x+5)(-2x-5)
Fp(x)= -4x2- 10x – 10x – 25
Fp(x) =-4x2 –20x–25
Fp(x)=-4x2- 20x –25

Fc(x)= (2x+5)/(-2x-5) = 2x+5 / -1(2x+5) y= -1 excepto en x=5/2

▪ Usabdo las leyes de los logaritmos, descomponer las siguientes expresiones:
1. LOGa(A*B*C) = LOGaA+LOGaB+ LOGaC
2. LOGaA3/B4= LOGaA3 - LOGaB4= 3 LOGaA- 4 LOGaB
3. LOGa[A2B3/C4D]= 2LOGaA+3 LOGaB-[4 LOGaC- LOGaD]
4. LOGa[A2B/C3] = 8 LOGaA+4 LOGaB- LOGaC
5. LOGa[pic]= 2/4 LOGaA +3/4 LOGaB-1/4 LOGaCExpresar como logaritmo de un solo número


1. LOGb x +LOGb3 + 2/3 LOG y = LOGb 3x (y2)1/2
2. 1/3 LOGbx – 2/5 LOGb y = LOGb[pic]
3. LOG2 (x2+5x+6) – LOG (x+2) = LOG2 [(x2+5x+6) /(x+2)]=(x+3)+(x+2)/(x+2)
4. (3/2 LOGa 100 – LOGa5)+ 1/3 LOGa27 =LOGa[pic]
5. Obtener x , x =9 LOGa9=9
X=9 LOGa 27/3 =9LOGa9=9

▪ Si el logaritmo LOGa7 =0.83 y el LOGa2 =0.12
Obtener:
1. LOGa49r: LOGa72=2(0.83)=.68
2. LOGa14 r: LOGa7*2= LOGa7+ LOGa 2 = 0.83+0.12= 0.95
3. LOGa56 r: LOGa(23*7)=3 LOGa2 + LOGa7=0.36+.83=1.19
4. LOGa98 r: LOGa(72*2) = 2 LOGa7 + LOGa2= .68+.12=.8
5....