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 positive)
Set the inner expression greater than or equal to zero
Subtract 3 from both sides
Combine like terms on the right side
Divide both sides by -1 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)
Divide
So that means x must be less 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: (-,3]
Notice if we graph , we get
notice how the graph never crosses the line
and we can see that x must be less than or equal to in order to lie on the graph. So this graphically verifies our answer.
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