___
The domain of f(x) = ³√x−4 is [4, ∞).

Question

Accepted Answer

Hey, everyone in this problem, we're asked to check whether the given statement is true or false. The statement we're given is that the domain of the 5th route of X -6 is the interval from six to infinity including six. OK. We have two answer choices. Option A, the statement is true and option B, the statement is false. So let's just rewrite what we have, right. The expression we have is the fifth root of X -6. And we want to evaluate the domain. Now we have to be a little bit care. OK. When we see roots, we automatically think of the rules we apply to square roots because that's what we're most familiar with. When we have a square root, there is a restriction, OK? We can't take the square root of a negative value. OK. That would give us a non-real number. So there is that restriction. However, in this case, we have a route of five. OK. So our root is odd when the root is odd, there is no restriction on the domain that we can take an odd route of a negative value. So there's no restriction on the domain that tells us that the domain is gonna be from negative infinity all the way to infinity. OK. So the statement we were given that the domain of the fifth route of the, of X -6 is the interval from six to infinity where we include six is going to be false. OK. That's answer choice. B because we have that odd route, we don't have a restriction on the domain. And so the domain instead should be all real numbers. That's it for this one. Thanks everyone for watching. I hope this video helped.

___ The domain of f(x) = ³√x−4 is [4, ∞).

Key Concepts

Domain of a Function

Cube Root Function

Vertical Shift

Watch next