Find the range of the function `f(x)=4cos^(3)x-8cos^(2)x+1`.

Explanation

`f(x)=4cos^(3)x-8cos^(2)x+1`
Let `g(x) =4x^(3)-8x^(2)+1` where xin [-1,1]
`therefore g(x) =12x^(2)-16x`
`g(x)=0`
`rArr x=0` or `x =(4)/(3)"in"[-1,1]`
Now `g(-1)=-11,g(0)=11,g(1)=-3`
Therefore the range of f(x) is [-11,1]