2. Solve the inequality $\arccos x \geq \arccos \left(x^{2}\right)$.
Solution. Let's write down the domain of definition: $|x| \leq 1,\left|x^{2}\right| \leq 1$.

The solution to this system of inequalities is the interval $[-1 ; 1]$. Note that the function $y=\arccos x-$ is decreasing. Therefore, the inequality from the condition is equivalent to the system of inequalities $x \leq x^{2},-1 \leq x \leq 1$. Its solution is the set $[-1 ; 0] \cup\{1\}$.