3. Given that $a \cos x + b \cos 2x \geqslant -1 (x \in \mathbf{R})$ always holds. Then the range of $a + b$ is $\qquad$
3. $[-1,2]$.

Let $\cos x=-\frac{1}{2} \Rightarrow a+b \leqslant 2$.
Also, when $a=\frac{4}{3}, b=\frac{2}{3}$,
$2 b \cos ^{2} x+a \cos x-b+1$
$=\frac{1}{3}(2 \cos x+1)^{2} \geqslant 0$.
Let $\cos x=1 \Rightarrow a+b \geqslant-1$.
Also, when $a=-1, b=0$, $a \cos x+b \cos 2 x=-\cos x \geqslant-1(x \in \mathbf{R})$. Therefore, the range of $a+b$ is $[-1,2]$.