2. Given the line $l: x+y-9=0$ and the circle $\odot M: 2 x^{2}+$ $2 y^{2}-8 x-8 y-1=0$, point $A$ is on $l$, and $B, C$ are two points on $\odot M$. In $\triangle A B C$, $\angle B A C=45^{\circ}, A B$ passes through the center $M$. Then the range of the x-coordinate of point $A$ is $\qquad$
2. $[3,6]$.

Let $A(a, 9-a)$. Then the distance from the center $M$ to the line $A C$ is $d=|A M| \sin 45^{\circ}$.
From the condition that the line $A C$ intersects with $\odot M$, we get $d \leqslant \frac{\sqrt{34}}{2}$.
Solving this, we get $3 \leqslant a \leqslant 6$.