Question

What is the domain of `g(t)=root4(t+4)`?

Answer 1

Let's look at the similarities between the something you're probably very familiar with, square roots, and this fourth root problem.

Consider the following example.

Determine the value of:

a) `(-2)^2`

b) `(-2)^3`

c) `(-2)^4`

Answer:

a) `(-2)(-2) = 4`

b) `(-2)(-2)(-2) = -8`

c) `(-2)(-2)(-2)(-2) = 16`

As you can see, there is a pattern here. Whenever the power is even, the answer will always be positive, while if it is odd it will be negative.

So, we can also conclude by this that `root(3)(-64)` is defined while `root(4)(-16)` isn't.

Hence, the function `g(t) = root(4)(t + 4)` is only defined when the number under the `4`th root is equal to or greater than `0`.

`0 <= root(4)(t + 4)`

`0 <= t + 4`

`-4 <= t`

So, the domain is `t >= -4`.

Hopefully this helps!