The range is f(x) ≥ 0 and the domain is all real numbers.
How to find the domain and range?
We want to find the dommain and range of the function:
f(x) = √(|x| - x)
Remember that the square root can only be positive, so the range is the set of all numbers equal to or larger than zero:
f(x) ≥ 0
For the domain. x can be any value, if x is positive, then:
f(x) = √(|x| - x) = √(x - x) = 0
For any positive x-value
if x is negative:
f(x) = √(|x| - x) = √(-x - x) = √(-2x)
and the negative sign does not causes problems because x is negative, so the domain is the set of all real numbers.
Complete question:
"Find the domain and range of f(x) = √(|x| - x)"