Question

Find the domain of the function:

h(y) = (y3-8)(y+2)-3

Answer 1

The domain is what you can put in for the independent variable which in this case is y. Since there is nothing restricting* y, the domain is all real numbers.
Usual restrictions are variables in the denominator (avoiding zero denominators), variables in radicals (avoiding even roots of negative numbers), logs of variables (avoiding undefined logs), etc.