Question

what is the domain of f(x)=^3 (square root of x+3) +1

Answer 1

\[\Large\rm f(x)=\sqrt[3]{x+3}+1\]Is this the function?
Cube root like that?

Answer 2

yes! :)

Answer 3

So you recall that we have a problem when we plug negatives into a `square` root, yes?\[\Large\rm \sqrt{-4}=no~real~solution\]But what about `odd` roots?
Like, do you understand how to calculate this?\[\Large\rm \sqrt[3]{-8}=?\]

Answer 4

not unless I have a calculator but yes I do if I have it!

Answer 5

lol, anyway.
\[\Large\rm (-2)(-2)(-2)=-8\]So the cube root of -8 is -2.
The cube root doesn't cause any problems for us.
So our domain will be all real numbers.

Answer 6

When looking for domain, try to look for problem areas.
If we had been given a `square` root instead of a `cube` root, then yes we would have some trouble area. But not in this case.