### Instruction: What is the domain of the function $$w(x) = \sqrt{x-2} + \sqrt[3]{x-3}~?$$ Express your answer in interval notation.### Response: I notice that the function w(x) has two parts: a square root and a cube root.
I know that the square root of a negative number is undefined, so I want to avoid that.
That means I need x-2 to be greater than or equal to zero, or x >= 2.
I also know that the cube root of any number is defined, even if it is negative.
So I don't have to worry about the cube root part of the function.
Therefore, the domain of the function is all the values of x that are greater than or equal to 2.
In interval notation, that would be [2, infinity).