The domain for the square root of (20-x) is x must be <= 20 real numbers. If x > 20, then the radicand becomes negative, which is fine, but not for real numbers. If x < 0, then 20 - (-x) becomes positive for all real number values for x.
Therefore, the domain can be stated as -∞ ≤ x ≤ 20.
You must follow the rule concerning the square roots: what is found under the radical sign is called radicand and it must be positive or zero.
The radicand is 20 - x.
`20 - xgt= 0`
Subtract 20 both sides:
`-x gt= - 20`
Multiply by -1:
`x =lt 20 ` (notice that the inequality has changed)
ANSWER: The domain of `sqrt (20-x)` is the interval `(-oo;20].`