f(x) = x - 9 4
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\(a,f\left(1\right)=3\cdot1^2+1+1=5\\ f\left(-\dfrac{1}{3}\right)=3\cdot\left(-\dfrac{1}{3}\right)^2-\dfrac{1}{3}+1=\dfrac{1}{3}-\dfrac{1}{3}+1=1\\ f\left(\dfrac{2}{3}\right)=3\cdot\left(\dfrac{2}{3}\right)^2-\dfrac{2}{3}+1=\dfrac{4}{3}-\dfrac{2}{3}+1=\dfrac{5}{3}\\ f\left(-2\right)=3\cdot\left(-2\right)^2-2+1=11\\ f\left(-\dfrac{4}{3}\right)=3\cdot\left(-\dfrac{4}{3}\right)^2-\dfrac{4}{3}+1=\dfrac{16}{3}-\dfrac{4}{3}+1=5\)
\(b,f\left(\dfrac{2}{3}\right)=\left|2\cdot\dfrac{2}{3}-9\right|-3=\dfrac{23}{3}-3=\dfrac{14}{3}\\ f\left(-\dfrac{5}{4}\right)=\left|2\cdot\left(-\dfrac{5}{4}\right)-9\right|-3=\dfrac{23}{2}-3=\dfrac{17}{2}\\ f\left(-5\right)=\left|2\left(-5\right)-9\right|-3=19-3=16\\ f\left(4\right)=\left|2\cdot4-9\right|-3=1-3=-2\\ f\left(-\dfrac{3}{8}\right)=\left|2\cdot\left(-\dfrac{3}{8}\right)-9\right|-3=\dfrac{39}{4}-3=\dfrac{27}{4}\)
\(c,x=0\Rightarrow y=2\cdot0^2-7=-7\\ x=-3\Rightarrow y=2\cdot\left(-3\right)^2-7=11\\ x=-\dfrac{1}{2}\Rightarrow y=2\cdot\left(-\dfrac{1}{2}\right)^2-7=\dfrac{-13}{2}\\ x=\dfrac{2}{3}\Rightarrow y=2\cdot\left(\dfrac{2}{3}\right)^2-7=-\dfrac{55}{9}\)

1. Ta có : 3x+12=0 <=> x= -4
bảng xét dấu:
x | -∞ -4 + ∞ |
3x+12 |
- 0 + |
f(x) >0 ∀ x ∈ (-4;+∞)
f(x) <0 ∀ x∈ (-∞;-4)
2. Ta có : -5x+9=0 <=> x= \(\frac{9}{5}\)
Bảng xét dấu:
x | -∞ 9/5 +∞ |
-5x+9 | + 0 - |
f(x) >0 ∀ x ∈ (-∞; 9/5)
f(x) <0 ∀ x ∈(9/5; +∞)
3. Ta có : -3x-9=0 <=> x= -3
x | -∞ -3 +∞ |
-3x-9 | + 0 - |
f(x) >0 ∀ x∈ (-∞; -3)
f(x) <0 ∀x∈ ( -3; +∞ )
4. Ta có : x (2x+4)=0
+, x=0
+, 2x+4=0 <=> x= -2
x | -∞ -2 0 +∞ |
x | - \(|\) - 0 + |
2x+4 | - 0 + \(|\) + |
f (x) | + 0 - 0 + |
f(x) >0 ∀ x ∈ (-∞; -2) \(\cup\) (0; +∞)
f(x) <0 ∀ x ∈ (-2;0)
5. Ta có: (x-2)(-x+4)=0
+, x-2=0 <=> x=2
+, -x+4=0 <=> x= 4
x | -∞ 2 4 +∞ |
x-2 | - 0 + \(|\) + |
-x+4 | + \(|\) + 0 - |
f(x) | - 0 + 0 - |
f(x) >0 ∀ x ∈ (2;4)
f (x) <0 ∀x∈ (-∞;2) \(\cup\)(4; +∞)
6. Ta có : (-4x+3)(x-6)=0
+, -4x+3=0 <=>x= \(\frac{3}{4}\)
+, x-6 =0 <=> x=6
x | -∞ 3/4 6 +∞ |
-4x+3 | + 0 - \(|\) - |
x-6 | - \(|\) - 0 + |
f(x) | - 0 + 0 - |
f(x) >0 ∀ x∈ (3/4;6)
f(x) <0 ∀ x∈ (-∞; 3/4) \(\cup\)(6;+∞)

F x = x - 9 5 5 + C