The domain of a function refers to the regions where the function is defined or has a value on a particular region.
4x2−1√9x2+1 has a domain defined on all set of real numbers because the function is defined on the set of real numbers when the denominator √9x2+1≥0.
√9x2+1≥0implies9x2+1≥0 which because of the square sign has a value for all values of x, be it negative or positive.