Domain and Range

Question

y=\sqrt[3]{x-5}

I had trouble formatting the question:

index=3

radicand= x-5

I am trying to understand domain and range for such an equation

I also know the answer for domain and range is all real numbers.

What am i missing. I thought the domain wound be x>5

Answer 1

The index is 3 which is an odd number.

When you have index as even number then you cannot have a negative number as radicand but there is no such restriction for odd indexes.

Hence the domain and range will be all real numbers.

( -3)^3 = -27

( -27)^1/3 = -3

But

( -27)^½ is undefined