For the given function we have:
- domain: x ≥ 0
- range: w(x) ≥ -4.
How to get the domain and range of the function?
Here we have the function:
[tex]w(x) = -(3x)^{1/2} - 4[/tex]
First, how do we get the domain?
Notice that we can only evaluate the square root in arguments equal or larger to zero (if we want a real outcome) then we need to have:
x ≥ 0.
Now, to get the range, maximum value is the one that we get when we evaluate in the minimum of the domain:
[tex]w(x) = -(3*0)^{1/2} - 4 = -4[/tex]
And as x increases, the value of w(x) decreases, then the range is:
R: w(x) ≥ -4.
If you want to learn more about domain and range:
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