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There are two families of functions with the same domain of f(x) = 2 · √x:

  1. Radical functions of the form f(x) = a · √(xⁿ).
  2. Radical-rational functions with no discontinuities for all x ≥ 0: g(x) = a · √(xⁿ / q(x)).

What kind of functions have the same domain of a given function?

In this problem we must determine the possible functions that share the same domain of a radical function: f(x) = 2 · √x. In accordance with function theory, the domain of a function is the set of x-values such that function exists.

Radical functions of the form f(x) = a · √x has domain in the interval [0, + ∞). Another function has the same domain if it has the same interval, there are two posibilities:

  1. Radical functions of the form f(x) = a · √(xⁿ).
  2. Radical-rational functions with no discontinuities for all x ≥ 0: g(x) = a · √(xⁿ / q(x)).

To learn more on radical functions: https://brainly.com/question/27847549

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