1
1)x-1≠0⇒x≠1
x∈(-∞;-1) U (-1;∞)
2)x²-3x-4≥0
x1+x2=3 U x1*x2=-4⇒x1=-1 u x2=4
x∈(-∞;-1] U [4;∞)
2
1)y=∛(x+1)
D(y)∈(-∞;∞)
x -9 -2 -1 0 7
y -2 -1 0 1 2
y>0 x∈(-1;∞)
2)y=2/x²
D(y)∈(-∞;0) U (0;∞)
x -2 -1 -1/2 1/2 1 2
y 1/2 2 8 8 2 1/2
y>0 x∈(-∞;0) U (0;∞)
3)y=x^4/2
D(y)∈(-∞;∞)
x -2 -1 0 1 2
y 8 1/2 0 1/2 8
y>0 x∈(-∞;∞)
3
1)x-3=125
x=128
2)ОДЗ x≥0
3-x-x²=x²
2x²+x-3=0
D=1+24=25
x1=(-1-5)/4=-1,5∉ОДЗ
х2=(-1+5)/4=1
5х - 8 + 3.6 = х^2 - 0.7х
- х^2 + 5х - 0.7х -4.4 = 0
х^2 - 5х + 0.7х +4.4 = 0
х^2 - 4.3х + 4.4 = 0
Д = (-4.3)^2 - 4*1*4.4 = 18.49 - 17.6 = 0.89
х1 = (4.3 - √0.89)/2
х2 = (4.3 + √0.89)/2