If the function \(f:(-\infty ,-1]\to (a,b]\) defined by \(f\left(x\right)={e}^{{x}^{3}-3x+1}\) is one - one and onto, th…

If the function \(f:(-\infty ,-1]\to (a,b]\) defined by \(f\left(x\right)={e}^{{x}^{3}-3x+1}\) is one - one and onto, then the distance of the point \(P(2b+4,a+2)\) from the line \(x+{e}^{-3}y=4\) is :

[JEE Main 2024, 31 Jan (Shift 2)]