### 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 think about what values of x make the function undefined or nonsensical.
One thing that can cause trouble is having a negative number inside a square root, since that would give an imaginary number.
So I want to avoid that by making sure that x-2 is not negative, or in other words, that x is not less than 2.
Another thing that can cause trouble is having a zero in the denominator of a fraction, since that would make the function undefined.
But I don't see any fractions in this function, so I don't have to worry about that.
The cube root of any number is well-defined, so I don't have to worry about that either.
So the only restriction on the domain is that x must be greater than or equal to 2.