Let f:[12 , 1]→[−1 , 1]  is given by f(x)=4x3−3x  then f−1(x)  is given by

Put x=cosθ⇒θ=cos−1x             y=f(x)=cos3θ⇒                   3θ=cos−1y             θ=13(cos−1y)             ∴f−1(x)=cos[13cos−1x]