Remember you cannot take the square root of a negative value. So that means the argument must be greater than or equal to zero (i.e. the argument must be non-negative)
Set the inner expression greater than or equal to zero
Add 4 to both sides
Combine like terms on the right side
So that means x must be greater than or equal to in order for x to be in the domain
So the domain in set-builder notation is
So here is the domain in interval notation: [4,)
Notice if we graph , we get
notice how the graph never crosses the line . So this graphically verifies our answer.
and we can see that x must be greater than or equal to in order to lie on the graph
(