How do you find the domain?

Question

h(x) = 1 / x^(1/2) - 5x^(1/4)

Tell me, don't just show the answer. The answers are in the back of my book.

Answer 1

The domain of a function is the set of possible inputs to that function. If given the function without its domain, you assume the domain is the largest set of numbers for which the function gives sensible outputs. Here, x=0 cannot be part of the domain, since that involves a division by zero, but the function is well-defined everywhere else. Thus the domain is all complex numbers except zero.

Edit: actually, I've assumed that the context is one that allows complex solutions. If you want only real solutions, then your domain is the positive reals, since x^(1/2) and x^(1/4) don't produce real answers when x<0.

Answer 2

Find all values of x that can't be true for h(x). x can't be less than 0, obviously becaue of the sqrt function, and it can't be equal to 0 either, because of division by zero. So the only values that are possible are positive numbers. In other words, {x | x > 0}.

Well, technically Pascal is right too, because of the complex numbers.

Answer 3

domain is the set of all possible values for x.
range is the set of all possible values for y

Answer 4

Dom h(x) = {x in R| x>0}