What is the domain of this function

f(x) = square root of -x +3
I know that the domain must be so that -x +3 is nonnegative.
The way i do it is -x+3 = 0, x = -3, therefore, x is greater or equal than -3. [-3, infinity) but in the textbook the answer is (-infinity, 0]

I think the only way that makes sense is if the problem is:
f(x) = sq rt(-x) + 3

To find the domain, write this inequality:
-x >= 0.........(>= means greater than or equal to)

Now solve for x by dividing by -1. When you divide an inequality by a negative number, don't forget to flip the inequality sign:
x<=0 or in interval notation (-infinity, 0]


If the problem is f(x) = sq rt(-x + 3), you would write the inequality:
-x + 3 >=0

And then solve for x:
-x >= -3
x<= 3 or (-infinity, 3]