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