*Xét dấu của các biểu thức:
a, f(x)= -2x + 3
b, f(x)= 4x – 12
c, f(x)= x² – 4
d, f(x)= -2x + 3/x – 2
e, f(x)= (2x – 1) × (x + 3)
f, f(x)= (-3x – 3) × (x + 2) × (x + 3)
g, f(x)= 2x + 1/(x – 1) × (x + 2)
h, f(x)= (4x – 1) × (x + 2) × (3x – 5) × (7 – 2x)
Đáp án:
b) \(\begin{array}{l}
f\left( x \right) > 0 \Leftrightarrow x \in \left( {3; + \infty } \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { – \infty ;3} \right)
\end{array}\)
Giải thích các bước giải:
a) BXD:
x -∞ 3/2 +∞
f(x) + 0 –
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { – \infty ;\dfrac{3}{2}} \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( {\dfrac{3}{2}; + \infty } \right)
\end{array}\)
b) BXD:
x -∞ 3 +∞
f(x) – 0 +
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( {3; + \infty } \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { – \infty ;3} \right)
\end{array}\)
c) BXD:
x -∞ -2 2 +∞
f(x) + 0 – 0 +
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { – \infty ; – 2} \right) \cup \left( {2; + \infty } \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { – 2;2} \right)
\end{array}\)
\(d)DK:x \ne 2\)
BXD:
x -∞ 3/2 2 +∞
f(x) – 0 + // –
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( {\dfrac{3}{2};2} \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { – \infty ;\dfrac{3}{2}} \right) \cup \left( {2; + \infty } \right)
\end{array}\)
e) BXD:
x -∞ -3 1/2 +∞
f(x) + 0 – 0 +
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { – \infty ; – 3} \right) \cup \left( {\dfrac{1}{2}; + \infty } \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { – 3;\dfrac{1}{2}} \right)
\end{array}\)
f) BXD:
x -∞ -3 -2 -1 +∞
f(x) + 0 – 0 + 0 –
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { – \infty ; – 3} \right) \cup \left( { – 2; – 1} \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { – 3; – 2} \right) \cup \left( { – 1; + \infty } \right)
\end{array}\)
\(g)DK:x \ne 1\)
BXD:
x -∞ -2 -1/2 1 +∞
f(x) – 0 + 0 – // +
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { – 2; – \dfrac{1}{2}} \right) \cup \left( {1; + \infty } \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { – \infty ; – 2} \right) \cup \left( { – \dfrac{1}{2};1} \right)
\end{array}\)
h) BXD:
x -∞ -2 1/4 5/3 7/2 +∞
f(x) – 0 + 0 – 0 + 0 –
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { – 2;\dfrac{1}{4}} \right) \cup \left( {\dfrac{5}{3};\dfrac{7}{2}} \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { – \infty ; – 2} \right) \cup \left( {\dfrac{1}{4};\dfrac{5}{3}} \right) \cup \left( {\dfrac{7}{2}; + \infty } \right)
\end{array}\)