inverted function

$$\\y=\sqrt{4-x}-3\qquad x\le4 \qquad y\ge-3 \\\\
y+3=\sqrt{4-x}\\\\
(y+3)^2=4-x\\\\
x=4-(y+3)^2\\\\
x=4-(y^2+6y+9)\\\\
x=4-y^2-6y-9\\\\
x=-y^2-6y-5\\\\
Inverse\;\;function\\\\
y=-x^2-6x-5 \qquad where \;\;\; x\ge-3\\\\$$

Here is the graph

https://www.desmos.com/calculator/rhqwzteqhk

Thanks a lot!!!