Verified answer

The domain is where the function exists. Many times we state a domain by stating where the function is not existing, with the assumption that it exists for all other real numbers. So we are looking for restrictions, e.g. denominators, radicands of even roots, and log objects.

In this expression there are 2 restrictions: denominator and radicand of a sqrt.

Thus, the restrictions are sqrt(x^2 - x - 30) =/= 0 and x^2 - x - 30 >= 0.

If we square the first restriction it almost looks like the second restriction and merely prohibits the inclusion of zero. Therefore we will work on the second restriction with only a > sign:

(x - 6)(x + 5 ) > 0

x > 6 or x < - 5. This is the domain.

x² - x - 30 > 0 ---> x < -5 or x >6