JEE Math Practice Question

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

1. A.$$2 \sqrt{1+e^6}$$
2. B.$$\sqrt{1+e^6}$$
3. C.$$3 \sqrt{1+e^6}$$
4. D.$$4 \sqrt{1+e^6}$$