Question

How do you find the domain of the function: `f(x) = sqrt(5-3x)`?

Answer 1

In your function you want to avoid a negative argumet of your square root so you set:
`5-3x>=0`
getting: `x<=5/3`
So your domain is all the real `x` that are less or equal to `5/3`.
Note that the negative `x` made me change the direction of my inequality.
You can have a look substituting values of `x` to confirm this;
try `x=2(>5/3)` (which is not acceptable) and `x=1(<5/3)` (which is ok) to confirm our reasoning.