### Instruction: What is the domain of the function $$w(x) = \sqrt{x-2} + \sqrt[3]{x-3}~?$$ Express your answer in interval notation.### Response: To find the domain of a function, I need to consider what values of x make the function undefined or invalid.
For example, I cannot take the square root of a negative number, so I need to avoid that.
The cube root of any number is always defined, so I don't have to worry about that.
The only thing that can make the function undefined is if the argument of the square root, x-2, is negative.
So I need to solve the inequality x-2 >= 0.
Adding 2 to both sides, I get x >= 2.
This means that the domain of the function is all the values of x that are greater than or equal to 2.
In interval notation, this is [2, infinity).