Ta có:
\(\left| {x + 1} \right| \ge 0,\forall x,\left| {x - 2} \right| \ge 0,\forall x\) \( \Rightarrow \left| {x + 1} \right|.\left| {x - 2} \right| \ge 0,\forall x \in \mathbb{R}\)
\(\left| {x + 1} \right|.\left| {x - 2} \right| = 0 \Leftrightarrow \left[ \begin{array}{l}x + 1 = 0\\x - 2 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = - 1\\x = 2\end{array} \right.\)
Vậy,
+) \(f\left( x \right) = 0\) khi \(x = - 1\) hoặc \(x = 2\)
+) \(f\left( x \right) > 0\) khi \(x \ne - 1\) và \(x \ne 2\)
