Question

Un mic ajutor la exercitiul 5, 6 si 7

Answer 1

Răspuns:

5.a)f(x)=√(x+1)/(x-1)

x-1≠0   x≠1

x+1=0   x= -1

Tabel de variatie

x   l -∞ ..................-1........0.......+1..............+∞

________________________________    

x+1    l -∞-   -   -    -0 +    +       +    +   +

_____________________________-------

x-1    l -∞-   -     -     -    -0++++++++++++++++

_______________________________

(x+1)/(x-1)+  +     + + 0-  - 0++++++=+++++++

iei in considerare intervalul pe care fractia e pozitiva.Acela e domeniul de definitie

D=(-∞ ,-1]U(1, +∞)    

b) f(x)=(x-2/(lxl -2)

Pui conditia ca lxl-2≠0

l xl≠2

D=R\{2}

c) f(x)=1/{x}

{x}≠0=> x≠0

D=R\{0}

d)f(x)=1/[x]

[x]≠0

=> x∉[0,1)

D=R\[0,1)

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6) a) f(x)=[x]  

f(x)=k  unde k∈Z=>

Imf= Z

b)f(x)=1/(x-2)

y=1/(x-2)

xy-2y=1

x=(1+2y)y=> y≠0=>

Im f=R*

c)f(x)=(x-2)/(3x-4)

y=(x-2)/(3x-4)

y(3x-4)=x-2

3xy-4y=x-2

3xy-x=4y-2

x(3y-1)=4y-2

x=(4y-2)/(3y-1)=. >  y≠1/3

D=R\[1/3}

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7)a.f(x)= lxl g(x)=x-1

lxl={x pt x≥0

{-x  pt  x<0

Suma

f(x)+g(x)={x+x-1=2x-1  pt  x≥0

{-x+x-1= -1  pt x<0

Produsul

f*g={x(x-1)=x²-x  pt x≥0

{-x(x-1) = -x²+x  pt x<0

Compusa fog

Faci mai intai semnul lui g

x-1≥0    x≥1

x-1<0    x<1

fog=x-1  pt x>1

fog= -(x-1)= 1-x pt x<1

7b)f(x)=∛(x+1)

g(x)=x³+1

suma f(x)+g(x)=∛(x+1)+x³+1

produsul f(x)*g(x)=∛(x+1)(x ³+1)

compusa

fog=∛(g+1)=∛(x³+1+1=∛(x³+2)

Explicație pas cu pas: