Question

Proszę o pomoc!!potrzebuje rozwiązania tych zadań na jutro gdzieś do godz.10
Zadania w załączniku

Answer 1

1.

a)

f(x) = (2x+4)/(3x+12)

3x+12 = 0

3x = -12  /:3

x = -4

D= R \ {-4}

b)

g(x) = (x^2 + 5x - 4)/(x^3 - 2x^2 - 4x + 8)

x^3 - 2x^2 - 4x + 8 = 0

x^2*(x-2) - 4(x-2) = 0

(x^2 - 4)(x-2) = 0

(x+2)(x-2)(x-2) = 0

x = -2  v  x = 2

D = R \ {-2,2} 

 

2.

f(x) = (x^2 - 6x + 8)/(x^2 - 4)

x^2 - 4 = 0

(x+2)(x-2) = 0

D = R \ {-2,2}

 

x^2 - 6x + 8 = 0

D(delta) = b^2 - 4ac = 36-32 = 4,  VD = 2

x1 = (-b-VD)/2a = (6-2)/2 = 2

x2 = (-b+VD)/2a = (6+2)/2 = 4

x1 = 2 nie należy do dziedziny,zatem:

MZ: 4

 

3.

F(x) = (2x+3)/(x+2),  dla x = V5 - 1

Z: x =/= -2

 

F(V5-1) = [2(V5-1)+3]/(V5-1+2) = (2V5-2+3)/(V5+1) = (2V5+1)/(V5+1) *(V5-1)/(V5-1) =

            = (2V5+1)(V5-1)/4 = (10-2V5+V5-1)/4 = (9-V5)/4

 

4.

MZ: 1, -2

D = R \ {-5, 0,3} 

np.:

f(x) = (x-1)(x+2)/(x+5)(x-0,3)

f(x) = (x^2 + x - 2)/(x^2 + 4,7x - 1,5)

 

5.

a)

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

                 x+1 = 0  => x = -1

                 x-1 = 0  => x = 1

                 D = R \ {-1,1}

= (x-1)(3x+2) = (x+1)(x-2) 

3x^2 + 2x - 3x - 2 = x^2 - 2x + x - 2

2x^2 = 0

x = 0

b)

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

               x-1 = 0  => x = 1

               x-2 = 0  => x = 2

               D = R \ {1,2}

(x-2+1)/(x-2) = 3/(x-1) 

(x-1)/(x-2) = 3x/(x-2)

(x-1)^2 = 3(x-2)

x^2 - 2x +1 = 3x - 6

x^2 - 5x + 7 = 0

D = 25 -28 = -3

D < 0 

a = 1 > 0  ramiona paraboli skierowane w gó

x e (-oo,1) u (2,+oo)

c)

(x-5)(4+2x)/(5x^2 +1) = 0

                5x^2 +1 > 0

                D = R

(x-5)(4+2x) = 0

x1 = 5 

=====

lub

4+2x = 0  /:2

x = -2

=====

x = -2,  v  x = 5

 

6.

a)

(x+1)/2 * 10x/(x^2 + x) =  

                                x^2 + x = 0

                                x(x+1) = 0

                                x = 0  v  x = -1

                                D = R \ {-1,0}

 = 5x(x+1)/x(x+1) = 5

b)

x^5/(2x-6) : x^3/(x^2 - 6x + 9) = 

                                2x-6 = 0  /:2

                                 x = 3

                                x^2 - 6x + 9 = 0

                                D(delta) = 36-36 = 0

                                x = 6/2 = 3 

                                D = R \ {3}

= x^5/(2x-6) *(x^2 - 6x + 9)/x^3 =x^2/2(x-3) * (x-3)^2 = x^2(x-3)/2 = (x^3 - 3x^2)/2