Question

What is the domain of the following function?

f(x) = √ -x + 2 - 1

Answer 1

You will have to use brackets to show where the square root ends

I suspect it is f(x) = √(-x+2) - 1 , or else why not combine the +2-1 ?

then the number under the square root must not be negative, that is ...
-x + 2 ≥ 0
-x ≥ -2
x ≤ 2

Answer 2

depends. How much of all that is under the radical sign?

Once you specify that, just remember that the domain of √u is u>=0.