1. The function
$$
y=4 \cos x+\cos 2 x(x \in \mathbf{R})
$$

has the range $\qquad$
$-1 .[-3,5]$.
Let $t=\cos x \in[-1,1]$. Then $y=2 t^{2}+4 t-1=2(t+1)^{2}-3$
Thus, the range of the function is $[-3,5]$.