9.090. $3^{\sqrt{x}}+3^{\sqrt{x}-1}-3^{\sqrt{x}-2}<11$.
Solution.

Domain of definition: $x \geq 0$.

From the condition $3^{\sqrt{x}}+\frac{3^{\sqrt{x}}}{3}-\frac{3^{\sqrt{x}}}{9}<11.11 \cdot 3^{\sqrt{x}}<9 \cdot 11,3^{\sqrt{x}}<3^{2}$. This is equivalent to the inequality $\sqrt{x}<2,0 \leq x<4$.

Answer: $\quad x \in [0 ; 4)$.