First:
![(f\circ g)(x)=\sqrt[]{-x-1}+9](https://img.qammunity.org/2023/formulas/mathematics/college/kn6n2tjaxs2ededav77n1btjkjxfe7p359.png)
The domain of this function is when the term under the root is positive or 0 because there is no root for a negative number in the real numbers, this only happens when:

Then, the domain is when x is:

Then, for the second part:
![(g\circ f)(x)=\sqrt[]{-(x+9)-1}=\sqrt[]{-x-10}](https://img.qammunity.org/2023/formulas/mathematics/college/i4dljcdhbejep2te915zf5k29ky0mpwdhv.png)
The domain for this function is only when the term under the root is positive or 0, so:

Then, the domain is:
