Find $f(E) $ and an explicit formula for $f^{-1}$ on $f(E)$.

Question

Find $f(E) $ and an explicit formula for $f^{-1}$ on $f(E)$.

1). $f(x)=x^2+2x-5$, $E=(-\infty,-6]$

Here what I tried if there is any mistakes please tell me,

First by looking at graphs I found,

$f(E)=[19,\infty)$ then I solved for $f(x)=y$ then I got two result $x=-1 \pm (y+6)^{1/2}$ Since question is said find a formula, I think both are correct on $f(E)$ but it is no sure!!! Is it correct?