Compare and Contrast Domains

Question

Compare and contrast the similarities and differences in the domains of the two following radical functions f(x) and g(x) below:

 

Answer 1

f(x) = √(x - 3)

We can only find square roots of nonnegative numbers

So, domain f = {x l x-3 ≥ 0} = [3, ∞)

--------------------------------------

g(x ) = ³√(x - 3)

We can find the cube root of any real number.

So, domain g = (-∞, ∞)