What is the domain of -3x^(1/3)+4x^(1/2)

The domain of the function would be [0, ∞)

This is because of the x^(1/2);  this is the same as the square root of x. Remember:  if x is under the square root, then x can't be negative because negatives do not have square roots.  X can be 0, because the square root of 0 is 0, and of course it can be positive.  So, x can be anywhere from 0 to infinity including 0.