What is the domain of Square root of 19-x?

domain of √(19 - x)

In order for this to give a real value, what is under the radical has to be non-negative. This includes zero and all positive values.

So let's solve the inequality of that expression greater than or equal to zero, and you have your answer:

19 - x ≥ 0

Subtract 19 from both sides:

-x ≥ -19

Multiply both sides by -1, which will flip the sign:

x ≤ 19

And that's your domain of x so the original expression gives a real value.

You can't take the square root of a negative number. Therefore the domain is the set of x such that 19 - x >= 0.

Solve that to find out what the corresponding x values that satisfy that are.