11.1. Solve the inequality $f(f(x))<(f(x))^{2}$, where $f(x)=2 x^{2}-1$.
Answer: $x \in(-1 ; 0) \cup(0 ; 1)$. Solution. Let $y=2 x^{2}-1$. Then

$$
2 y^{2}-1<y^{2} \Leftrightarrow-1<y<1 \Leftrightarrow 0<2 x^{2}<2 \Leftrightarrow 0<|x|<1
$$