Question

I need to find the domain for this

Answer 1

`\large\boxed{Domain:\ x\in\mathbb{R}\to\text{the set of all real numbers}}`

Explanation:

The domain of roots:

`\sqrt[n]{p(x)}`

If n is an odd number, then p(x) can be any real number.

If n is an even number, then p(x) must be a non-negative number.

We have

`f(x)=\sqrt[3]{2x^2-3x-9}`

n = 3 → odd number.

Therefore the domain is the set of all real numbers.