What is the domain of square root of x square minus six?

Answer 1

Within reason, it can be anything. The answer depends on what you want the codomain (range) to be.

• If the codomain is to be integers, the domain must be {x | x = n2 -2n + 7 where n is in N}
• If the codomain is to be the real numbers, the domain must be {x | x is in R, x2 ≥ 6},
• If the codomain is the set of complex numbers, then the domain is R.
• There is a more complicated answer if the codomain is to be the set of rational numbers.

But, essentially, the answer is "it depends".