f(x) = 3x^5/(2x - x^1/2)

Question

What is the domain of the function?

Answer 1

Factor the denominator to find all of its zeros.  Each of those must be excluded from the domain. THIS MUST BE DONE FOR ANY RATIONAL ALGEBRAIC FUNCTION, before any cancellation of identical factors (no such cancellation occurs, in this case, anyway).

 

A rational algebraic function is continuous on its domain (Fact from Calculus).