Đáp án:
Giải thích các bước giải:
a)f(x)=(x-1)(5-10x)
Cho x-1=0⇒ x=1
5-10x=0⇒ \(x=\frac{1}{2}\)
Vậy f(x)>0⇒ S=\((\frac{1}{2};1)\)
f(x)<0⇒ S=\((-\infty;\frac{1}{2})∩(1;+\infty )\)
f(x)≥0⇒ S=\([\frac{1}{2};1]\)
f(x)≤0⇒ S=\((-\infty;\frac{1}{2}]∩[1;+\infty )\)
b)f(x)=\(\frac{(2x+6)(4-x)}{2x-1}\)
Cho 2x+6=0⇒ x=-3
4-x=0⇒ x=4
2x-1=0⇒ x=\(\frac{1}{2}\)
Vậy f(x)>0⇒ S=\((-\infty;-3)∩(\frac{1}{2};4)\)
f(x)<0⇒ S=\((-3;\frac{1}{2})∩(4;+\infty)\)
f(x)≥0⇒ S=\((-\infty;-3]∩(\frac{1}{2};4]\)
f(x)≤0⇒ S=\([-3;\frac{1}{2})∩[4;+\infty)\)
2)a)(2x+2)(5-x)<0
Cho 2x+2=0⇒ x=-1
5-x=0⇒ x=5
Vậy S=\((-\infty;-1)∩(5;+\infty)\)
b)\(\frac{(x+3)(2-x)}{4x-7}≥0\)
Cho x+3=0⇒ x=-3
2-x=0⇒x=2
4x-7=0⇒ x=\(\frac{7}{4}\)
Vậy S=\((-\infty;-3]∩(\frac{7}{4};2]\)
