Question

How do you find the domain of `f(x)= 5+sqrt(9-x)`?

Answer 1

You must ensure that the argument of your square root is always bigger or equal to zero (you cannot find a real solution of a negative square root).
Translated in maths means that you want:
`9-x>=0` or
`x<=9` that is your domain.
So, you can choose 9 and numbers smaller than 9.

Graphically:
graph{5+sqrt(9-x) [-28.86, 28.88, -14.43, 14.43]}