3
a)(x²-2x-3)/x<0<br>x²-2x-3=0
x1+x2=2 U x1*x2=-3⇒x1=-1 U x2=3
x=0
_ + _ +
--------------(-1)--------------(0)-----------------(3)--------------------
x∈(-∞;-1) U (0;3)
b)(x-5)/(x+4)-((2x-4)/(x+5)≥0
(x²-25-2x²+8x-8x+16)/(x+4)(x+5)≥0
(x²+9)/(x+4)(x+5)≤0
x²+9>0 при любом х⇒(x+4)(x+5)<0<br>x=-4 U x=-5
x∈(-5;-4)
4
a)f(x)=√x/(x-7)
x/(x-7)≥0
x=0 x=7
+ _ +
------------[0]------------------(7)----------------
x∈(-∞;0] U (7;∞)
б)f(x)=√9x-x³
9x-x³≥0
x(3-x)(3+x)≥0
x=0 x=3 x=-3
+ _ + _
-------[-3]----------[0]---------------[3]---------------------
x∈(-∞;-3] U [0;3]
в)f(x)=√x/(x-7)-3√(9x-x²)
{x/(x-7)≥0
{9x-x²≥0
x∈(-∞;0] U (7;∞) U (-∞;-3] U [0;3]⇒x∈(-∞;-3] U {0}
5
f(x)=(x²+1)/x
a)f(x)=0
x²+1=0
x²+1>0 при любом х⇒x∈∅
б)(x²+1)/x>0
x²+1>0 при любом х⇒x>0
x∈(0;∞)
в)(x²+1)/x<0<br>x²+1>0 при любом х⇒x<0<br>x∈(-∞;0)