### 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 need to find the set of values of x that make the function w(x) well-defined and real.
For the first square root term, I know that the radicand x-2 must be nonnegative, otherwise I would get an imaginary number.
So I need x-2 >= 0, or x >= 2.
For the second cube root term, I don't have any restriction on the radicand x-3, because any real number can be raised to the 1/3 power and still be real.
So I don't need to worry about this term.
Therefore, the domain of w(x) is just the set of x values that satisfy x >= 2, or in interval notation, [2, infinity).