y=cos^x-3cosx+a
=(cosx-3/2)^2-9/4+a
cosx=1,ymin=a-3=-3/2,a=3/2
cosx=-1,ymax=a+2=7/2
-3/2<=y<=7/2
a^y
(3/2)^(-3/2)<=a^y<=(3/2)^(7/2)