Đáp án:
a) BXD:
x -∞ -1 1/2 +∞
f(x) - 0 + 0 -
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { - 1;\dfrac{1}{2}} \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { - \infty ; - 1} \right) \cup \left( {\dfrac{1}{2}; + \infty } \right)
\end{array}\)
b) \(DK:x \ne 2\)
BXD:
x -∞ 1/3 2 +∞
f(x) - 0 + // -
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( {\dfrac{1}{3};2} \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { - \infty ;\dfrac{1}{3}} \right) \cup \left( {2; + \infty } \right)
\end{array}\)
c) \(DK:x \ne 4\)
BXD:
x -∞ -5 2 4 +∞
f(x) - 0 + 0 - // +
d) \(\begin{array}{l}
f\left( x \right) > 0 \Leftrightarrow x \in \left( { - \infty ; - \dfrac{1}{3}} \right) \cup \left( {0;4} \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { - \dfrac{1}{3};0} \right) \cup \left( {4; + \infty } \right)
\end{array}\)
Giải thích các bước giải:
d) BXD:
x -∞ -1/3 0 4 +∞
4x - / - 0 + / +
3x+1 - 0 + / + / +
4-x + / + / + 0 -
f(x) + 0 - 0 + 0 -
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { - \infty ; - \dfrac{1}{3}} \right) \cup \left( {0;4} \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { - \dfrac{1}{3};0} \right) \cup \left( {4; + \infty } \right)
\end{array}\)
\(e)DK:x \ne 1\)
BXD:
x -∞ -3 0 1 +∞
f(x) - 0 + 0 - 0 +
\(\begin{array}{l}
KL:f\left( x \right) > 0 \Leftrightarrow x \in \left( { - 3;0} \right) \cup \left( {1; + \infty } \right)\\
f\left( x \right) < 0 \Leftrightarrow x \in \left( { - \infty ; - 3} \right) \cup \left( {0;1} \right)
\end{array}\)
